Factoring Review (M1)

Factoring Review (M1)

A short review of factoring methods.

GCF: The Greatest Common Factor

• Break down each term into simplest pieces

• AKA Prime Factorization

• "Pull out" the common pieces each term shares

Multiple Choice

What is the GCF of 18k and 15k³

• 3k²
• 3k³
• 3k
• 5k

Multiple Choice

Factor out the GCF:
10x³ - 15x

• x(10x² - 15)
• 5x(2x² - 3)
• 5(2x³ - 3x)
• 5x²(10x - 3)

Difference of Squares

• Simple pattern --> Look for 2 terms only with subtraction

•  $a^2-b^2=\left(a+b\right)\left(a-b\right)$  

• 
  

Multiple Choice

Factor:
x² - 9

• (x + 3)(x - 3)
• (x + 3)²
• (x - 3)²
• (x+3)(x+3)

Multiple Choice

Which of the following is a difference of perfect squares?

• x² - 18
• 4x² + 36 
• 9x² - 100
• x² + 4

Multiple Choice

What are the factors of
25x² - 81?

• (5x - 9)(5x + 9)
• (5x - 9)(5x - 9)
• (5x + 9)(5x + 9)
• Cannot be factored

Standard Trinomial: a = 1

• Automatic -->

   $x^2+bx+c=\left(x\ \ \ \ \ \ \ \right)\left(x\ \ \ \ \ \ \ \right)$  

• Choose numbers that multiply to get c but also add to get b

Multiple Choice

Factor

k²+7k+10

• (k+2)(k+5)

• (k-2)(k-5)

• (k+10)(k+4)

• (k+2)(k-5)

Multiple Choice

Factor:
x² - 5x - 14

• (x - 2)(x + 3)
• (x - 2)(x + 7)
• (x + 2)(x - 7)
• (x - 2)(x - 3)

Multiple Choice

Factor completely.
k² -2k - 24

• (k+4)(k-6)
• (k+4)(k+6)
• (k+6)(k-1)
• (k-4)(k+6)

Slide and Divide

• Multiply the leading coefficient (the "a" number) by the constant "c"

• Convert from

   $ax^2+bx+c$  to a simpler version  $x^2+bx+c$  

• Divide by "a" at the end

Multiple Choice

Factor
3v² - 4v - 7

• (3v-7)(v+1)
• 3(v-7)(v-1)
• (3v+1)(v-9)
• (3v+1)(v-10)

Multiple Choice

Factor:
10x² + 9x - 7

• (5x + 10)(2x - 7)
• (10x + 2)(x - 3)
• (5x + 3)(2x + 1)
• (5x + 7)(2x - 1)