1. Algebra 3 Warm-Up 2.2 List the factors of 36 1, 36 2, 18 3, 12 4, 9 6,

2. Algebra 3 Lesson 2.2 Objective: SSBAT factor a polynomial by factoring out the GCF and using Difference of Squares. Standards: M11.D.2.2.2

3. Monomial An expression with 1 term 5x 2 -3mn 3 k 8 Binomial An expression with 2 terms 4x – 2 15x 3 + 8y Trinomial An expression with 3 terms 8x 5 – 5w 3 + 2 16 – 3x + 5m 4

4. Factors  The numbers used in a multiplication problem  5 x 3 = 15, 5 and 3 are the factors of 15 List the Factors of 24  1, 2, 3, 4, 6, 8, 12, 24

5. Greatest Common Factor (GCF) The biggest number that is a factor of all of the numbers in a set. Find the GCF of 18 and 45  Factors of 18: 1, 2, 3, 6, 9, 18  Factors of 45: 1, 3, 5, 9, 15, 45  GCF of 18 and 45 is 9

6. Finding the GCF of expressions (variables) Example: 6x 4 y and 10x 2 1.Find the GCF of the Coefficients (numbers in front) 2.Find the GCF of each variable piece by  Look at only one set of like variables at a time  If the variable does not appear in all of the terms do not use it in the GCF  If the variable appears in every term use the one with the smaller exponent in the GCF

7. Find the GCF of each. 1.2 5x 2 y 4 and 10x 3 y  GCF: 5x 2 y 2. 21mn 2 k and 10m 2 n 2  mn 2

8. 3.12x 4 y, 9x 5 y 2, 21x 7 yw 3  GCF: 3x 4 y 4.m 5 n 3 k 2 and mnk  GCF: mnk

9. Factoring  Rewriting an expression as a multiplication problem  2 · 5 is the factored form of 10  3(x + 4) is the factored form of 3x + 12

10. Factoring Out the GCF 1. Find the GCF of all of the terms in the polynomial 2.Write the GCF outside of the parentheses 3.Divide each term of the polynomial by the GCF and write this expression inside the parentheses

11. Examples: Factor out the GCF of each. 1. 2w 3 + 10w The GCF is 2w = 2w(w 2 + 5)

12. Examples: Factor out the GCF of each. 2. 18n 3 + 9n 2 – 24n The GCF is 3n = 3n(6n 2 + 3n – 8)

13. Examples: Factor out the GCF of each. 3. –20x 6 + 12x 3 – 4x The GCF is 4x  When the lead coefficient is Negative factor out the negative as well = –4x(5x 5 – 3x 2 + 1)

14. Examples: Factor out the GCF of each. 4.15mn 3 – 9m 2 n 4 + 18m 3 n 5 The GCF is 3mn 3 = 3mn 3 (5 – 3mn + 6m 2 n 2 )

15. Perfect Square  A number that you can take the Square Root of  1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121,…  Perfect Square expressions are x 2, x 4, x 6, …

16. Difference of Squares  An expression of the a 2 – b 2  Perfect Square – Perfect Square Examples: x 2 – 4 m 2 – 25 9x 2 – 1 *** x 2 + 4 is NOT a difference of squares because of the PLUS ***

17. Factoring a Difference of Squares a 2 – b 2 = (a + b)(a – b)  Take the square root of each term  Add the 2 square roots in one ( )  Subtract the 2 square roots in another ( )

18. Factor each Difference of Squares 1. x 2 – 64 = ( + )( – ) 2. 81 – x 2 =( + )( – ) x x 88 9 9x x

19. Factor each Difference of Squares 3. 4x 2 – 25 = ( + )( – ) 4. w 2 – y 2 = ( + )( – ) 2x 55 ww y y

20. Factor each Difference of Squares 5. 49x 2 – 1 =( + )( – ) 6. x 2 – 130 Can’t Do – It is NOT a Difference of Squares  130 is not a perfect square 7. x 2 + 9 Can’t Do – It is NOT a Difference of Squares  It’s Plus not Minus 7x 11

21. 8. w 6 – 196 = (w 3 + 14)(w 3 – 14) 9. 100x 22 – y 16 = (10x 11 – y 8 )(10x 11 + y 8 )

22. On Your Own. 1.Factor out the GCF. 8x 3 – 20x 5 + 2x 2 2.Factor the Difference of Squares. 36x 2 – 49 3.Factor out the GCF. 12m 3 n 5 – 24mn 4 – 30m 6 n 4.Factor the Difference of Squares. 81 – m 12 = 2x 2 (4x – 10x 3 + 1) = (6x + 7)(6x – 7) = (9 + m 6 )(9 – m 6 ) = 6mn(2m 2 n 4 – 4n 3 – 5m 5 )

23. Homework Worksheet 2.2