Unit 5 Pt. 2 Review - Factoring Polynomials

Unit 5 Pt. 2 Review - Factoring Polynomials

Factoring out a GCF

• Find the greatest number that all of the terms can be divided by equally (Hint: use desmos!)

• Put the GCF outside the parenthesis, and what is left over inside the parenthesis

Multiple Choice

What is the GCF of the polynomial?

 $6x^4-12x^2+3x$  

• 3x

• 3

•  $x^4$  

•  $6x^4$  

Multiple Choice

Which option shows the factored form of

 $8x^2+32$  using the GCF?

•  $8\left(x^2+4\right)$  

•  $4\left(2x^2+8\right)$  

•  $8x\left(x+4\right)$  

•  $8x^2\left(4\right)$  

Factoring by grouping:

1.Multiply a(c)
2. Find 2 numbers that multiply to be a(c) and add to be b
3. Expand b to be the two terms from step 2
4. Group the polynomial into 2 parts and factor the GCF out of each part

Example of factoring by grouping

Multiple Select

Select all the factors of the following polynomial

 $x^2-6x-40$  

• (x-10)

• (x+4)

• (x-4)

• (x-2)

• (x+10)

Multiple Choice

Rewrite in factored form:

 $x^2+10x+16$  

• (x+8)(x+2)

• (x-8)(x-2)

• (x+4)(x+6)

• (x+8)(x-8)

Factoring to solve for zeros

• Factor the polynomial (look for a gcf first)

• Set all of the factors equal to zero and then solve

Multiple Select

Select all of the zeros for the polynomial

 $4x^2-1=0$  

•  $-\frac{1}{2}$  

•  $\frac{1}{2}$  

•  $\frac{1}{4}$  

•  $-\frac{1}{4}$  

• 0

Multiple Select

Select all of the zeros for the polynomial:

 $x^2+8x+15$  

• x=-5

• x=-3

• x=5

• x=3

• x=0

Multiple Select

Select all of the zeros for the polynomial

 $100x^4-25x^2$  

•  $x=0$  

•  $x=\frac{1}{2}$  

•  $x=-\frac{1}{2}$  

•  $x=-4$  

•  $x=4$