Chapter 7 Factoring Polynomials Review Text page 453

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) 3 x 3 & 6 x 2 a) 4 x 2 & 5 y 3

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

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

5 3 Ex 1 b. ) Factor 4 x - 6 x + 14 x • Find the GCF – 2 x • Divide GNF by both terms – 4 x - 6 x + 14 x 2 x 2 x 2 x 4 2 • Multiply the GCF and the Quotient

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

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

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

Ex 3 a) Factor by Grouping Factor: 12 a 3 – 9 a 2 + 20 a – 15 • Group terms that have a common factors • Find the GCF • Divide the GCF by both terms • Multiply GCF and the Quotient

Ex 3 b) Factor by Grouping Factor: 9 x 3 – 18 x 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 + 8 x + 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 2+ 14 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 2 + 19 x + 60 • y 2 + 6 y + 8

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

Factor y 2 - 11 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 - 7 x + 10 • x 2 - 5 x + 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. 3 a) Factor the following Polynomial 2 • X - 5 x -24

Factor a 2 + 29 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 )

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

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

Homework Practice 7 -3 wkst (p. 476) • Day 1 – # 20 -31 • Day 2 – # 33 -49 (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.

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

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

Factor 10 + 11 x - 6 x 2 • 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 6 x and 10 • Test for answer

Ex. ) Factor the following Polynomials pages 480 -482

Homework Activities • Day 1 • Day 4 – Page 484 • #’s 1 -24 even • Day 2 – Page 484 • #’s 1 -24 odd • Day 3 – Page 484 • #’s 34 -51 • Day 5 – Page 484 • #’s 55 -63 • Day 6 – Quiz page 489

7 -5