Chapter 7 Factoring Polynomials

Review Text page 453 – # 1-29

7-1 Factors and GCF EX. 1 Writing Prime Factorization a)60 b)40 c)19

Finding GCF Ex. 2 Finding GCF (2 methods) a)24 & 60 b)18 & 27

GCF of Monomials Ex. 3 Find the GCF a)3x 3 & 6x 2 a)4x 2 & 5y 3

Homework Pr 7-1 (p 459) – # 1-15; 28-30

7-2 Factor by GCF Ex 1a. Simplify 5x + 10x Find the GCF – 5x Divide GNF by each term – 5x + 10x 5x 5x - x + 2 Multiply the GNF and the Quotient 5x(x+2)

Ex 1b.) Factor 4x - 6x + 14x Find the GCF – 2x Divide GNF by both terms – 4x - 6x + 14x 2x 2x 2x Multiply the GCF and the Quotient 53 42

Ex 1c)Factor 8a bc - 12ab c Find the GNF Divide the GCF by both terms Multiply GCF and the Quotient 2 22

Ex 2a) Factor a Common Binomial Factor: 7 (x- 3) – 2x ( x – 3) Find the GCF Divide the GNF by both terms Multiply GNF and the Quotient

Ex 2b) Factor a Common Binomial Factor: 9x (x + 4) – 5 ( 9x + 4) Find the GCF Divide the GNF by both terms Multiply GNF and the Quotient

Ex 3a) Factor by Grouping Factor: 12a 3 – 9a a – 15 Group terms that have a common factors Find the GCF Divide the GCF by both terms Multiply GCF and the Quotient

Ex 3b) Factor by Grouping Factor: 9x 3 – 18x 2 + x – 2 Group terms that have a common factors Find the GCF Divide the GCF by both terms Multiply GCF and the Quotient

Homework Pr 7-2 (p. 467) Day 1 o # 1-26 Day 2 o # 27-54

7-3 Factoring x 2 + bx + c We know that when we FOIL the follow, (x + 3)(x + 5) = x + 8x + 15 Now we are going to work backwards using – Coefficient 8 is the sum of 3 and 5 – Constant 15 is the product of 3 and 5

Factor y y + 40 Since the coefficient is positive, list the positive factors of 40 – 40: 1&40, 2&20, 4&10, 5&8 Find the pair of factors whose sum is 14 – 4&10 Include each factor in separate binomials along with the variable – (y+4)(y+10)

Ex.1) Factor the following Trinomials x x + 60 y 2 + 6y + 8

Homework Practice 7-3 (page 476) #’s 1-3

Factor y y + 18 Since the coefficient is negative, list the negative factors of 18 – -1&-18,-2&-9,-3&-6 Find the paid of factors whose sum is -11 – -2&-9 Include each factor in separate binomials along with the variable – (y-2)(y-9)

Ex 2.) Factor the following Trinomials x 2 - 7x + 10 x 2 - 5x + 6

Homework Practice 7-3 (page 476) #’s 7-9

Factor x 2 - x - 20 List factors of -20 – 1&20, 2&10, 4&5 Find the pair of factors with the sum of -1 – You may have to mentally test sum using combinations of signs – +4 & -5 Include each factor in separate binomials along with the variable (x + 4) ( x – 5)

Ex.3a) Factor the following Polynomial X 2 - 5x -24

Factor a a - 30 List factors of -30 Find the pair of factors with the sum of 29 You may have to mentally test sum using combinations of signs Include each factor in separate binomials along with the variable (a ) ( a )

Ex.3b) Factor the following Polynomial X 2 + 7x -18

Homework Practice 7-3 (page 476) #’s 10-15

Homework Practice 7-3 wkst (p. 476) Day 1 – # Day 2 – # (Quiz)

7-4 Factoring ax 2 + bx + c Trinomials with this pattern can be factored but it takes patients and trial and error to achieve the correct factorization. Not only do you have to use factors of the constant c, but the number of the coefficient of the higher power whose sum equals the middle coefficient.

Factor 2x + 7x - 9 Because the constant is negative, on factor will be negative and the other will be positive. List possible factors of 2x and possible factors of -9. – 2x : 2x & x – -9 : 1&9, 3&3 (1 factor positive, 1 negative) Test the possibilities to see which produces the correct coefficient 7x – Since 2x only has 2 factors, they must be part of the solution (2x + )(x - ) – Test the 2 sets of factors for -9 to determine the correct combinations (2x + 1 )(x - 9 ); (2x + 9 )(x - 1 ) (2x + 3 )(x - 3 ); (2x + 3 )(x - 3) Answer – (2x + 9 )(x - 1 ) 2 2 2

Factor 14x -17x +5 Because the constant is negative, on factor will be negative and the other will be positive. List possible factors Test the possibilities 2

Factor x - 6x Arrange terms in descending order – Trinomial could be factored in ascending order, but it may be helpful to keep the same form as we are used to working with. Because the coefficient is positive, both factors will be positive List possible factors of 6x and 10 Test for answer 2

Ex. ) Factor the following Polynomials pages

Homework Activities Day 1 – Page 484 #’s 1-24 even Day 2 – Page 484 #’s 1-24 odd Day 3 – Page 484 Activities Day 4 – Page 484 #’s Day 5 – Page 484 #’s Day 6 – Quiz page 489

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