4.10B - Factoring Polynomials

4.10B - Factoring Polynomials using MAM

How to Find a GCF in a Polynomial

• Break down every term into prime factors. (Expand it)

• Look for factors that appear in every single term to determine the GCF.

• Factor the GCF out from every term in front of parentheses and group the leftovers inside the parentheses

• Multiply each term to simplify.

Multiple Choice

Factor completely:

16x² - 20xy

(Use your calculator to find the GCF)

Ex: Press MATH, Right Arrow ->, #9

gcd(16, 20)

• $4xy\left(4x-5\right)$
  

• $4x\left(4x-5y\right)$

• $4x^2\left(4-5y\right)$

• 2(duck)

The Box Method

• Label your trinomial as M.A.M

• Multiply both M-terms

• Find two factors that give you 'M' when you multiply and 'A' when you add.

• Write each term in the box with their variable

• Find the GCF "going down" and "across"

• Write the outside terms in factored form

The Box Method

• Label your trinomial as M.A.M

• Multiply both M-terms

• Find two factors that give you 'M' when you multiply and "A" when you add.

• Put each term in the box with their variable

• Find the GCF "going down" and "across"

• Write the outside terms in factored form

You try!

Factor using GCF.

Multiple Choice

Factor

 $x^2+7x+10$  

• (k+2)(k+5)

• (k-2)(k-5)

• (k+10)(k+4)

• (k+2)(k-5)

Multiple Choice

A rectangle has an area of  $6x^2-x-12$ and a width of  $2x-3$ . Which expression represents the length of the rectangle?

•  $4x-15$  

•  $4x-9$  
  

•  $3x-4$  
  

•  $3x+4$  
  

Multiple Choice

Which of the following is a prime factor of

 $6x^2+13x-5$  ?

• 2x - 5

• 3x + 1

• 6x - 5

• 2x + 5

Multiple Choice

Factor Completely:

 $5x^2-11x+6$  

• (5x+6)(x-1)

• (5x-6)(x-1)

• (2x-7)(x-3)

• (5x-6)(x+1)