Factoring By Lindsay Hojnowski (2014) Buffalo State College 04/2014L. Hojnowski © Click here to play tutorial introduction Greatest Common Factor (GCF) Monomial x Polynomial Binomial x Trinomial Trinomial Difference of Perfect Squares (DOPS) Binomial x Binomial

Learning Objectives Students will be able to multiply monomials by polynomials 90% of the time. Students will be able to utilize the traditional and the box method to find the products of polynomials with 85% degree of accuracy. The learner will be able to multiply special products. Students will be able to factor using the greatest common factor (GCF) and grouping 85% of the time. 04/2014L. Hojnowski © Aim for the Target

Learning Objectives Continued… Students will be able to factor trinomials (a = 1 and a > 1) with 85% degree of accuracy. Students will be able to factor using the difference of two perfect squares (DOPS) 90% of the time. Students will be able to factor completely 80% of the time. 04/2014L. Hojnowski © Aim for the Target

Menu 04/2014L. Hojnowski © 2014 Vocabulary 4 Multiplying a Monomial and a Polynomial- Example 1 References Question #1 Question #2 Question #3 Question #6 Question #4 Question #5 Question #7 Multiplying a Monomial and a Polynomial- Example 2 and 3 Multiplying Binomials – Two Different Methods Multiplying Binomials – Traditional Distributing Example 1 Multiplying Binomials – Box Method Example 1 Multiplying Binomials – Traditional Distributing Example 2 and 3 Multiplying Binomials – Box Method Example 2 and 3 Multiplying Binomials – Using Two Different Methods Special Products- Example 2 and 3 GCF Factoring- Steps GCF Factoring- Example 2 and 3 Grouping Conditions Grouping- Steps Grouping- Examples Special Products- Example 1 Trinomials (a = 1)- Steps Trinomials (a = 1)- Example 2 and 3 Trinomials (a > 1)- Steps Trinomials (a > 1)- Example 2 and 3 DOPS- Conjugates Conjugate Examples Review of Perfect Squares DOPS- Examples Factor Completely- Steps Factor Completely- Example 2 Factor Completely- Example 3 and 4 Question #8 Question #9 Question #10 DOPS- Example 1 and 2

Vocabulary A.Constant: a number that does not change; it remains the same  Example: any number; 2, -8 B.Variable: a letter that represents a number, it’s value will vary  Example: any letter; x, b, n, etc. C.Term: a variable, constant, or a product of variables and constants  Example: 4x 2, 2xy, y, 4 D.Polynomial: the sum of many terms  Example: 8x 2 + x + 2, -2x 2 + 4x - 3 E.Monomial: a polynomial with 1 term  Example: 4x 2, 6xy, 16 F.Binomial: a polynomial with 2 terms  Example: x 2 + 4, x + 6 G.Trinomial: a polynomial with 3 terms  Example: 7x 2 - x - 18, y 2 + 2y /2014L. Hojnowski © Vocabulary

Multiplying a Monomial and a Polynomial- Example 1 04/2014L. Hojnowski © Reminder: When multiplying variables, add the exponents. **When there is no exponent written, the exponent is 1** Example 1: x (4x 2 + 3x + 2) x (4x 2 + 3x + 2) 4x 3 + 3x 2 + 2x Monomial x Trinomial Distribute Combine like terms (when necessary)

Multiplying a Monomial and a Polynomial- Example 2 and 3 04/2014L. Hojnowski © Example 2: 2/3np 2 (20p 2 + 9n 2 p – 12) (Distribute) 40/3np 4 + 6n 3 p 3 – 8np 2 (Can’t combine) Example 3: 2b (b 2 + 4b + 8) – 3b(3b 2 + 9b + 18) (Distribute) 2b 3 + 8b b – 9b 3 – 27b 2 – 54b (Combine like terms) -7b 3 – 19b b

Multiplying Binomials- Two Different Methods Traditional Distributing: (x+1) (x + 2) x (x + 2) + 1 (x + 2)  Distribute x 2 + 2x + 1x + 2  Combine like terms x 2 + 3x /2014L. Hojnowski © Box Method (Modeling): x 2 + 1x + 2x + 2 x 2 + 3x +2 Example: (x+1) (x + 2)

Multiplying Binomials- Traditional Distributing Example 1 04/2014L. Hojnowski © Example 1: (x+ 2) (x + 4) (x+ 2) (x + 4) x (x + 4) + 2 (x + 4) Distribute x 2 + 4x + 2x + 8Combine like terms x 2 + 6x + 8 -To find the product of two binomials- you must distribute each term in the first set of ( ) to each term in the second set of ( )

Multiplying Binomials- Traditional Distributing Example 2 and 3 04/2014L. Hojnowski © Example 2: (2y - 5) (y - 6) (2y - 5) (y - 6) 2y (y - 6) – 5 (y - 6) 2y 2 – 12y – 5y y 2 – 17y To find the product of two binomials- you must distribute each term in the first set of ( ) to each term in the second set of ( ) Example 3: (3x - y) (4x + 2y) (3x - y) (4x + 2y) 3x (4x + 2y) - y (4x + 2y) 12x 2 + 6xy - 4xy – 2y 2 12x 2 + 2xy – 2y 2 Distribute Combine like terms

Multiplying Binomials- Box Method Example 1 04/2014L. Hojnowski © Box Method is also known as modeling Example 1: Find the product: (8m – 1)(8m + 1) 64m 2 + 8m – 8m – 1 64m 2 – 1 ** Multiply the product of each box! ** Rewrite the terms in each box and combine like terms

Multiplying Binomials- Box Method Example 2 and 3 04/2014L. Hojnowski © Example 2: Find the product: (k + 4)(5k - 1) 5k k – k – 4 5k k - 4 Example 3: Find the product: (2a - 4)(3a - 6) 6a 2 – 12a– 12a a 2 – 24a + 24

Multiplying Binomials- Using Two Different Methods 04/2014L. Hojnowski © Traditional Distributing: (2b + 4) (2b 2 - 8b + 3) 2b (2b 2 - 8b + 3) + 4 (2b 2 - 8b + 3) (Distribute) 4b 3 – 16b 2 + 6b + 8b b + 12 (Combine like terms) 4b 3 – 8b b + 12 Box Method (Modeling): 4b 3 – 16b 2 + 6b + 8b b b 3 – 8b b + 12 Find the product using two different methods: (2b + 4) (2b 2 - 8b + 3) Should be the same answer (if they are not you made a mistake)

Special Products- Example 1 04/2014L. Hojnowski © Example 1: (x – 6) 2 (x - 6)(x – 6) x(x – 6) – 6(x – 6) x 2 – 6x - 6x + 36 x 2 – 12x Square of sum and differences means write the binomial two times and distribute (using either traditional method or box method) Find each product: Write it twice Multiply/distribute Combine like terms

Special Products- Example 2 and 3 04/2014L. Hojnowski © Example 2: (m 2 – 2) 2 (m 2 – 2)(m 2 – 2) m 2 (m 2 – 2) – 2(m 2 – 2) m 4 – 2m 2 – 2m m 4 – 4m Example 3: ((3/4)k + 8) 2 ((3/4)k + 8)((3/4)k + 8) (3/4)k ((3/4)k + 8)+ 8((3/4)k + 8) (9/16)k 2 + 6k + 6k + 64 (9/16)k k + 64 Special Products

GCF Factoring- Steps 04/2014L. Hojnowski © Steps to GCF Factoring STEPS: 1)Find the GCF by taking the lowest exponent (and finding a common factor of the two terms) 2)Write the GCF before parentheses 3)Divide each term of the polynomial by the GCF A)Divide coefficients B)Subtract the exponents Example 1: Factor the following polynomial using GCF 7y 2 – 21y7y 2 – 21y GCF = 7y7y 7y7y ( y – 3) GCF out front

GCF Factoring- Example 2 and 3 04/2014L. Hojnowski © Example 3: Factor the following polynomial using GCF 2x 2 + 4x + 62x 2 + 4x + 6 GCF = (x 2 + 2x + 3) GCF out front Example 2: Factor the following polynomial using GCF 27x 2 – 18x 3 GCF = 9x 2 9x 2 9x 2 9x 2 (3 + 2x) GCF out front

Grouping Conditions 04/2014L. Hojnowski © A polynomial can be factored by grouping ONLY if all of the following conditions exist: 1)There are four or more terms 2)Terms have a common factor that can be grouped together 3)There are 2 common factors that are identical to each other (the parentheses match) Grouping Example

Grouping- Steps 04/2014L. Hojnowski © Steps to factoring by grouping STEPS: 1)Group the terms with common factors 2)Factor the GCF from each group 3)Rewrite the final answer as a (binomial)(binomial) Directions: Factor the following polynomial. Show all your work. Example 1: 4qr + 8r + 3q +6 4r (q + 3) + 3 (q + 3) (4r + 3) (q + 3) GCF = 4r GCF = 3 These should match

Grouping- Examples 04/2014L. Hojnowski © Example 2: 3x 3 – 6x 2 + x - 2 GCF = 3x 2 GCF = 1 3x 2 (x - 2) + 1 (x - 2) These should match (3x 2 + 1) (x - 2) Directions: Factor the following polynomials. Show all your work. Example 3: 2mk – 12m – 7k + 42 GCF = 2m GCF = -7 2m (k - 6) - 7(k - 6) These should match (2m - 7) (k - 6)

Trinomial (a = 1)- Steps 04/2014L. Hojnowski © Steps to Factoring a=1 Trinomials STEPS: 1)When the leading coefficient is 1, ask yourself “what numbers multiply to the last term and adds to the middle term?” 2)Rewrite the trinomial as a polynomial with 4 terms (the middle term will get replaced by the 2 new terms that add to it) 3)Factor the polynomial by grouping Example 1: x x + 24x x + 24 Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24x 2 + 4x + 6x , 6 are factors of 24 that add to 10 x (x + 4) + 6 (x + 4) (x + 6)(x + 4)

Trinomial (a = 1)- Example 2 and 3 04/2014L. Hojnowski © Example 2: x 2 – 2x - 63 Factors of -63: 1, 3, 7, 9, 21, 63 (one has to be negative) 7, -9 are factors of -63 that add to -2 x 2 – 2x - 63 x 2 + 7x - 9x – 63 x (x + 7) - 9 (x + 7) (x - 9)(x + 7) Directions: Factor the following polynomials. Show all your work. Example 3: x 2 + x - 56 Factors of -56: 1, 2, 4, 7, 8, 14, 28, 56 (one has to be negative) 8, -7 are factors of -56 that add to 1 x 2 + x - 56 x 2 + 8x - 7x – 56 x (x + 8) - 7 (x + 8) (x - 7)(x + 8)

Trinomial (a > 1)- Steps 04/2014L. Hojnowski © STEPS: 1)First see if a GCF can be factored out (this is ALWAYS the 1 st step of factoring) 2)Find the product of a and c from the trinomial (make sure you include the sign of each number) 3)Think of a pair of numbers whose sum is equal to ac 4)Break up the middle term into those two numbers 5)GCF Factor twice (grouping) Recall: Standard from of a quadratic equation is y = ax 2 + bx + c Example 1: 2x 2 + 5x + 3 a = 2 c = 3, ac = 6 Factors of 6: 1, 2, 3, 6 2, 3 are factors of 6 that add to 5 2x 2 + 2x + 3x + 3 2x (x + 1) + 3 (x + 1) (2x + 3)(x + 1)

Trinomial (a > 1)- Example 2 and 3 04/2014L. Hojnowski © Example 2: 4x x + 5 a = 4 c = 5, ac = 20 Factors of 20: 1, 2, 4, 5, 10, 20 -2, -10 are factors of 20 that add to -12 4x 2 - 2x – 10x + 5 2x (2x - 1) - 5 (2x - 1) (2x - 5)(2x - 1) Example 3: 3x x + 10 a = 3 c = 10, ac = 30 Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 2, 15 are factors of 30 that add to 17 3x 2 + 2x + 15x + 10 x (3x + 2) + 5 (3x + 2) (x + 5)(3x + 2)

DOPS- Conjugates 04/2014L. Hojnowski © When two binomials look the same, but have different signs between the two terms, the binomials are called conjugates Conjugates

Conjugate Examples 04/2014L. Hojnowski © For each of the following binomials, write the conjugate: Expression: x 2 – 3 Conjugate:x Expression: a + b Conjugate:a + b The conjugate can be very useful because when you multiply something by its conjugate, you get squares like this… (a + b)(a – b) = a 2 – b 2

DOPS- Example 1 and 2 04/2014L. Hojnowski © Directions: Multiply each of the following. Example 1: (y – 5) (y + 5) y Example 2: (8x - y) (8x + y) 64x 2 – y 2 This expression is called DOPS (Difference of Perfect Squares)- **Notice the minus sign in between the terms and that both terms are perfect squares)

Review of Perfect Squares 04/2014L. Hojnowski © Let’s review the perfect squares 1- 15: Perfect Square

DOPS- Examples /2014L. Hojnowski © Directions: Factor each of the following. Example 3: x (x – 9) (x + 9) Example 5: 16h 2 – 9a 2 (4h – 3a)(4h + 3a) Example 4: 64 - y 2 (8 – y) (8+ y) Example 6: 100g 2 –h 2 (10g – h)(10g + h) DOPS

Factoring Completely- Steps 04/2014L. Hojnowski © Steps to Factoring Completely STEPS: 1)Factor out the GCF (if there is one) 2)Factor the polynomial (DOPS, Trinomial (a = 1 or ac method), Grouping) Example 1: Factor completely 2x 2 + 4x - 16 GCF = (x 2 + 2x - 8 ) GCF out front 2 (x 2 + 2x - 8)  you can factor what is in the parentheses (Trinomial) Factors of -8: 1, 2, 4, 8 (one has to be negative)  4, -2 are factors of -8 that add to 2 x 2 + 4x – 2x - 8 x (x + 4) - 2 (x + 4) 2(x - 2)(x + 4) Don’t forget the GCF out front!

Factoring Completely- Example 2 04/2014L. Hojnowski © Example 2: Factor completely 10y 3 – 35y y GCF = 5y 5y 5y 5y5y (2y 2 – 7y + 6) GCF out front 5y (2y 2 – 7y + 6)  you can factor what is in the parentheses (Trinomial ac) a = 2 c = 6, ac = 12  Factors of 12: 1, 2, 3, 4, 6, 12  -3, -4 are factors of 12 that add to -7 2y 2 – 4y – 3y + 6 5y(2y - 3)(y - 2) 2y (y - 2) - 3 (y - 2) Don’t forget the GCF out front!

Factoring Completely- Example 3 and 4 Example 3: Factor completely 27g 3 – 3g GCF = 3g 27g 3 – 3g 3g 3g 3g (9g 2 – 1) GCF out front 3g (9g 2 – 1)  Factor parentheses (DOPS) 3g (3g – 1) (3g + 1) 04/2014L. Hojnowski © Example 4: Factor completely 2y 4 – 50 GCF = 2 2y 4 – (y 4 – 25) GCF out front 2 (y 4 – 25)  Factor parentheses (DOPS) 2 (y 2 – 5) (y 2 + 5)

Quiz Question #1 04/2014L. Hojnowski © Simplify: (3/4)m 2 n (16m 3 n 2 – 4m 2 n 3 + 6mn) a. a. 16m 6 n 2 – 3m 4 n 3 + 6m 2 n b. 12m 5 n 3 + 3m 3 n 3 + (9/2)m 3 n 2 b. c. c. 12m 6 n 2 + 3m 4 n 3 + 6m 2 n d. 12m 5 n 3 – 3m 4 n 4 + (9/2)m 3 n 2d.

Try Again… 04/2014L. Hojnowski © When distributing, you forgot to multiply the fraction and 16. Also, when you multiply variables, add the exponents! Quiz Question #1 Quiz Question #2 Try Again

Try Again… 04/2014L. Hojnowski © Quiz Question #1 Quiz Question #2 Try Again Be careful of your signs!

Try Again… 04/2014L. Hojnowski © Quiz Question #1 Quiz Question #2 Try Again When you multiply variables, add the exponents! Be careful of your signs and multiplication.

Correct!! 04/2014L. Hojnowski © You distributed correctly. You’re signs are perfect. Great job! Quiz Question #1 Quiz Question #2 Smile

Quiz Question # 2 04/2014L. Hojnowski © Find the product of (4x – 3y)(3x + 2y) a.a. 12x 2 – 6y 2 b. 12x 2 – 9xy - 6y 2 c. 12x 2 – 9xy + 6y 2 d. 12x 2 – xy - 6y 2b. c. d.

Try Again… 04/2014L. Hojnowski © These binomials are not conjugates of each other, thus you have to multiply each and every term. Quiz Question #1 Quiz Question #2 Try Again Quiz Question #3

Try Again… 04/2014L. Hojnowski © Try Again Quiz Question #1 Quiz Question #2 Quiz Question #3 Careful when you combine like terms. Go back and check your work.

Try Again… 04/2014L. Hojnowski © Try Again Quiz Question #1 Quiz Question #2 Quiz Question #3 Be careful of your signs and check your answer when you combine like terms.

Correct!! 04/2014L. Hojnowski © Smile Quiz Question #1 Quiz Question #2 Quiz Question #3 You multiplied correctly! Awesome job keeping track of your signs and combining like terms.

Quiz Question # 3 04/2014L. Hojnowski © What is the product of ((2/5)y – 4) 2 ? a.a. (4/10)y 2 – (8/5)y - 16b. (4/10)y 2 – (16/5)y + 16b. c. c. (4/25)y 2 – (16/5)y + 16 d. (4/25)y d.

Try Again… 04/2014L. Hojnowski © Quiz Question #2 Quiz Question #1 Try Again Quiz Question #4 Quiz Question #3 Double check your multiplication. A negative number times a negative number is a POSITIVE number. Also, be sure you multiplied every term.

Try Again… 04/2014L. Hojnowski © Try Again Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Double check your multiplication. Be sure you are not adding.

Correct!! 04/2014L. Hojnowski © Smile Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 You multiplied correctly! Awesome job keeping track of your signs and combining like terms.

Try Again… 04/2014L. Hojnowski © Try Again Be careful, you can’t just square both terms. You have to write what is in the parentheses twice, and then distribute. Also, a negative number times a negative number is a POSITIVE number. Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3

Quiz Question # 4 04/2014L. Hojnowski © What is the correct factoring of 4k 3 + 6k 2 + 2k? a. a. 2k (2k 2 + 3k) b. 2k (2k 2 + 3k + 1) c. 2 (2k 3 + 6k 2 + k) d. 4k (k 2 + 2k + 1)b. c. d.

Try Again… 04/2014L. Hojnowski © Careful when you take out the GCF. Try to multiply it out again to see what you’re answer will be. This might help you find your mistake. Try Again Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5

Correct!! 04/2014L. Hojnowski © Smile Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 You found the correct GCF and divided the GCF out perfectly. Great job remembering the 1.

Try Again… 04/2014L. Hojnowski © Try Again Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Careful with your GCF. What else do the terms have in common?

Try Again… 04/2014L. Hojnowski © Try Again Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Careful with your GCF. Is 4k a factor of each and every one of the terms? Also, make sure you are dividing the GCF out not subtracting.

Quiz Question # 5 04/2014L. Hojnowski © Factor: 3dt – 21d – 5t + 35 a.a. (3d + 5)(t – 7)b. (3d - 5)(t – 7)c. (3d + 5)(t + 7)d. (3d - 5)(t + 7)b. c. d.

Try Again… 04/2014L. Hojnowski © Careful when you take out the GCF of the second group. To check your work, you could multiply it out to see what your mistake could be. Try Again Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6

Correct!! 04/2014L. Hojnowski © Smile Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Awesome job factoring by grouping!

Try Again… 04/2014L. Hojnowski © Try Again Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Careful when you divide out the GCF from both groups. More specifically, be careful of your signs!

Try Again… 04/2014L. Hojnowski © Try Again Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Careful when you divide out the GCF. More specifically, be careful of your signs!

Quiz Question # 6 6. Factor: a 2 + 8a - 48 a. a. (a + 3)(a – 16) b. (a - 3)(a + 16) c. (a + 4)(a + 12) d. (a - 4)(a + 12) b. c. d. 04/2014L. Hojnowski ©

Try Again… 04/2014L. Hojnowski © Try Again Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Quiz Question #7 3 times -16 is -48, but does = +8? Try to find factors that multiply to -48 that add to 8.

Try Again… 04/2014L. Hojnowski © Try Again Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Quiz Question #7 -3 times 16 is -48, but does = +8? Try to find factors that multiply to -48 that add to 8.

Try Again… 04/2014L. Hojnowski © Try Again Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Quiz Question #7 4 times 12 is 48, but we want -48. Try to find factors that multiply to -48 that add to 8. You’re factors add to 16 right now.

Correct!! 04/2014L. Hojnowski © Smile Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Quiz Question #7 Awesome job finding factors and having the correct signs!

Quiz Question # 7 7. Factor: 3x 2 – 17x + 20 a. a. (3x + 4)(x – 5) b. (3x - 5)(x – 4) c. (3x + 5)(x + 4) d. (3x - 4)(x - 5)b. c. d. 04/2014L. Hojnowski ©

Try Again… 04/2014L. Hojnowski © Multiply out your answer. Compare it with the original question. This might help you find your mistake. Try Again Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Quiz Question #7

Correct!! 04/2014L. Hojnowski © Smile Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Quiz Question #7 You factored correctly! Great!

Try Again… 04/2014L. Hojnowski © Try Again Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Quiz Question #7 Multiply out your answer. Compare it with the original question. This might help you find your mistake.

Try Again… 04/2014L. Hojnowski © Try Again Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Quiz Question #7 Multiply out your answer. Compare it with the original question. This might help you find your mistake.

Quiz Question # 8 8. Factor, completely when necessary. 4a a. a. (4a – 5)(4a + 5) b. (2a + 5)(2a + 5) c. (2a – 5)(2a + 5) d. (4a – 25)(4a + 25)b. c. d. 04/2014L. Hojnowski ©

Try Again… 04/2014L. Hojnowski © Be careful, if this is a DOPS question you need to take the square root of both terms in the binomial. Try Again Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Quiz Question #7 Quiz Question #8

Try Again… 04/2014L. Hojnowski © Try Again Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Quiz Question #7 Quiz Question #8 Be careful to be a difference of perfect squares you need one – and one +.

Correct!! 04/2014L. Hojnowski © Smile You factored correctly! There is no GCF to be taken out. Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Quiz Question #7 Quiz Question #8

Try Again… 04/2014L. Hojnowski © Try Again Careful 4 is not a factor of 25, thus the GCF is not 4. Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Quiz Question #7 Quiz Question #8

Quiz Question # 9 9. Factor, completely when necessary. 9m a. a. (3m – 12)(3m + 12) b. (3m + 12)(3m + 12) c. 9(m ) d. 9(m – 4)(m + 4)b. c. d. 04/2014L. Hojnowski ©

Try Again… 04/2014L. Hojnowski © Be careful. This does look like a difference of two perfect squares, but your first thought should always be GCF. Try Again Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Quiz Question #7 Quiz Question #8 Quiz Question #9

Try Again… 04/2014L. Hojnowski © Try Again Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Quiz Question #7 Quiz Question #8 Quiz Question #9 Be careful. This does look like a difference of two perfect squares, but your first thought should always be GCF. Also, to be a difference of perfect squares you need one – and one +.

Try Again… 04/2014L. Hojnowski © Try Again Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Quiz Question #7 Quiz Question #8 Quiz Question #9 Be careful. Is your answer factored completely? What does it mean to be factored completely?

Correct!! 04/2014L. Hojnowski © Smile Great job taking out the GCF and factoring what was left correctly! Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Quiz Question #7 Quiz Question #8 Quiz Question #9

Quiz Question # Factor, completely when necessary. 25b b 2 – 5b a. a. 5b (5b – 1)(b + 1) b. (5b – 1)(b + 1) c. 5b (5b 2 + 4b - 1) d. 5b (5b + 1)(b - 1)b. c. d. 04/2014L. Hojnowski ©

Correct!! 04/2014L. Hojnowski © Smile Great job dividing out the GCF and factoring what was left! Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Quiz Question #7 Quiz Question #8 Quiz Question #9 Quiz Question #10

Try Again… 04/2014L. Hojnowski © You factored correctly, but you forgot one thing. What do you have to remember to bring down? Try Again Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Quiz Question #7 Quiz Question #8 Quiz Question #9 Quiz Question #10

Try Again… 04/2014L. Hojnowski © Try Again Your GCF is correct and you divided it out correctly. What does it mean to factor completely? Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Quiz Question #7 Quiz Question #8 Quiz Question #9 Quiz Question #10

Try Again… 04/2014L. Hojnowski © Try Again Careful of your signs when you factor! Quiz Question #2 Quiz Question #1 Quiz Question #4 Quiz Question #3 Quiz Question #5 Quiz Question #6 Quiz Question #7 Quiz Question #8 Quiz Question #9 Quiz Question #10

References McGraw-Hill Companies. (2014). Glencoe Algebra 1 Common Core Edition. New York: McGraw Hill. Seminars.usb.ac.ir. (2011). Hitting the objectives, Retrieved on September 14 th, 2012, from facilitator. facilitator Smiley Face, Retrieved on September 14 th, 2012, from ges/happy-face1.png. ges/happy-face1.png Wee, E. (2011). Try again, Retrieved on September 15 th, 2012, from 3-caring-for-children.html. 3-caring-for-children.html 04/2014L. Hojnowski © Reference from the dictionary