Factoring GCF, Difference of Squares, and Trinomials Review

Factoring GCF, Difference of Squares, and Trinomials Review

Factoring a GCF

Lesson 5.1

Steps to Factor Using the GCF

• Find the GCF of the numbers (use Desmos if you need).

• Find the GCF of the variables. If a variable is in EVERY term, use the one with the smallest exponent.

• Write the GCF in front of parentheses.

• Divide each term in the problem by the GCF (dividing the coefficients and subtracting the exponents), and write the remainder inside the parentheses.

Multiple Choice

 $5x^4y^2-45xy^4+20y^2$  Try it! Choose the correctly factored problem.

•  $5y^2\left(5x^4y-9xy^3+8y\right)$  

•  $5y^2\left(x^5y-9xy^4+4y\right)$  

•  $20y\left(x^4y-9xy^3+4y\right)$  

•  $5y^2\left(x^4-9xy^2+4\right)$  

Factoring Difference of Squares

Lesson 5.2

Steps to Factor with Difference of Squares

• Check to make sure you have a difference of squares! You should have two perfect squares separated by a subtraction sign.

• Take the square root of each term.

• Write your two factors using the rule: a²-b² = (a+b)(a-b).

Multiple Choice

 $16x^4-9y^4$  Try it! Choose the correctly factored polynomial.

•  $\left(4x^2-3y^2\right)^2$  

•  $\left(4x^2+3y^2\right)\left(4x^2-3y^2\right)$  

•  $\left(16x^2+9y^2\right)^2$  

•  $\left(4x^4+3y^4\right)\left(4x^4-3y^4\right)$  

Factoring a Trinomial with a=1

Lesson 5.3

Steps to Factoring Trinomial (a=1)

• Trinomial: ax²+bx+c

  Goal: Find factors of c that add up to b.

• Use the graphic organizer flow chart to figure out the signs of the numbers.

• If needed, make a table of possible factors that multiply to your c value. Find the pair that add up to b.

Multiple Choice

 $n^2+3n-18$  Try it! Choose the correctly factored trinomial.

•  $\left(n+3\right)\left(n-6\right)$  

•  $\left(n+3\right)\left(n+6\right)$  

•  $\left(n-3\right)\left(n+6\right)$  

•  $\left(n-9\right)\left(n+2\right)$  

Factoring a GCF First

Steps to Factor a GCF out First

• Factor the GCF following the same methods as before (find the GCF of the numbers, of the variables, the divide it from each term)

• If what is left in parentheses is a difference of squares, factor what is in parentheses using that method. Write the GCF in front.

• If what is left in parentheses is a trinomial, factor what is in parentheses using that method. Write the GCF in front.

GCF with Difference of Squares

1. Factor out GCF

2. Factor remaining difference of squares

GCF with Trinomial (a=1)

1. Factor out GCF

2. Factor remaining trinomial

Multiple Choice

 $125x^2-5$  

Factor out the GCF first. Then, factor using another method.

•  $5\left(3x+4\right)\left(3x-4\right)$  

•  $5\left(5x+1\right)\left(5x-1\right)$  

•  $\left(5x-1\right)^2$  

•  $5\left(25x+1\right)^2$  

Multiple Choice

 $4x^3-20x^2+24x$  

Factor out the GCF first. Then, factor using another method.

•  $4x\left(x-2\right)\left(x-3\right)$  

•  $4\left(x-2\right)\left(x+3\right)$   

•  $2x\left(x+6\right)\left(x+4\right)$  
  

•  $4x\left(x-12\right)\left(x+2\right)$  
  

Don't forget!!

• If a polynomial cannot be factored, it is called PRIME!

• (x+2)(x+2) is the same as (x+2)²

Multiple Choice

 $125x^2-5$  

Factor out the GCF first. Then, factor using another method.

•  $5\left(3x+4\right)\left(3x-4\right)$  

•  $5\left(5x+1\right)\left(5x-1\right)$  

•  $\left(5x-1\right)^2$  

•  $5\left(25x+1\right)^2$