Warm Up: Review Multiply the polynomials: 1. (x – 4)(2x – 2) 3. 3x(2x 2 y + 2xy + 3y + 4) 2. (3x – 1)(x + 3) 4. 2x(15x + 4) + 3(15x + 4)

FACTORING September 17th

GCF (Greatest Common Factor) The Greatest Common Factor (GCF) of two or more numbers is the largest number that can divide into all of the numbers. To find the GCF, start by writing out the prime factorization. What factors do the numbers have in common? Circle these then multiply the common factors to get your answer.

Find the GCF 1. 40a 2 b and 48ab a 3 b 4 and 3a 5 b 3. 7x 2 y 2 and 10xy 3

Remember Distributive Property? Multiply: 3x(10x+2y) We can work backwards to factor. What if I gave you 30x 2 + 6xy? How would you factor this?

“ Undistribute ” or Factor Using the GCF Find the GCF then use the distributive property to factor out the GCF. What are we really doing? Take out the GCF and then write your “leftovers” on the inside. Always check your answer by using the distributive property Example 1: Factor 15x 2 y 5 + 5xy 3

Factor Using the GCF 1. 12a 2 b + 24a – 48b 2. 18z 3 + 9z 2 – 6z

Factor the GCF 1. 3x 3 y – 9x 2 y x 3 – 8x x

Practice Find the GCF of 120x 2 y 5 and 60x 4 y 5 A. 60x 4 y 5 B. 60x 2 y 5 C. 2x 4 y 5 D. 2x 2 y 2

Practice What is the GCF of the terms of A. 2B. 4C. 2cD. 4c

Practice Factor 15x 2 -12x + 5 A. 5(3x 2 – 2x + 1) B. x(15x 2 – 12x + 5) C. (x + 3)(x – 5) D. Prime

Practice Factor 12x 3 y 2 – 9x 2 y 4 + 6x 2 y. A. 3x 2 y(4xy – 3y 3 + 2) B. 3x 2 y(4x – 3y 3 + 2y) C. xy(12x 2 y – 9xy 3 + 6x) D. 3xy(4x 2 y – 3xy 3 + 2x)

Factoring by Grouping You can try to factor by grouping when your polynomial has FOUR terms. 1. Always look for a GCF first! 2. Then group your terms in pairs using parenthesis. 3. Find the GCF for each binomial. 4. Your answer will be (GCF’s)(leftovers). ***Your leftovers must match***

Factoring by Grouping Always look for a GCF first! Then group your terms in pairs using parenthesis. Find the GCF for each binomial. Your answer will be (GCF’s)(leftovers). Your leftovers must match example 1: 12x 3 + 3x x + 5

Factoring by Grouping Practice 1. 8x 2 + 8xy + 2y 2 + 2xy 2. 2m 3 + 8m 2 + 9m + 36

Factoring a Trinomial when a = 1 Standard From for Trinomial: ax 2 + bx + c X – puzzle: example: x 2 + 5x + 4 **Two numbers whose product is 4 and sum is 5

Factor 3. x 2 - 4x – x 2 - 8x + 7

Patterns to Notice If c is positive (x 2 + bx + c), then both binomials will have the sign of b. If c is negative (x 2 + bx – c), then you will have one binomial with addition, and one with subtraction.

Which factoring process should I use? Always check for a GCF! And if there is one, factor (un-distribute) it FIRST. After it’s factored out or if there isn’t one, see how many terms it has. 4 terms  factor by grouping 3 terms  factor the trinomial (like we did today)

Homework Factoring Worksheet