Factoring Polynomials

Factor out a GCF ONLY:  $8x+12$  

• 8(x+12)

• 4(2x+3)

• 2(4x+6)

• There's no GCF

 Factor out GCF ONLY:  $2x^3-8x^2+24x$ 

•  $2x\left(x^2-4x+12\right)$  

•  $2\left(x^3-4x^2+12x\right)$  

•  $2x^2\left(x-4+24\right)$  

• There's no GCF

Factor out GCF ONLY: $-4x^3-16x^6$  

•  $-4x^3\left(4x^3\right)$  

•  $-4x^3\left(1-4x^3\right)$  

•  $-4x^3\left(1+4x^3\right)$  

• There's no GCF

 $x^2+x-12$  Completely Factor:

• (x + 4)(x - 3)

• (x + 6)(x - 2)

• (x - 4)(x - 3)

• Can't Factor

Completely Factor: $2x^2+3x-9$  

• (x + 3)(x - 3)

• 2x(x+3)(x-3)

• (2x - 3)(x + 3)

• Can't Factor

 $6x^5-26x^4+8x^3$  Completely Factor:

•  $2x^3\left(3x-1\right)\left(x-4\right)$  

•  $\left(3x-1\right)\left(x-4\right)$  

•  $2x^3\left(3x+4\right)\left(x-1\right)$  

• Can't Factor

 $x^2+16x+48$  Completely Factor:

• (x + 8)(x + 6)

• (x + 8)(x + 2)

• (x + 12)(x + 4)

• Can't Factor

 $7x^2-4x-3$  Completely Factor:

• 7x(x+3)(x-1)

• (7x + 3)(x - 1)

• (7x - 3)(x + 1)

• Can't Factor 

 Completely Factor: $-2x^7+24x^6+90x^5$ 

•  $-2x^5\left(x+3\right)\left(x-15\right)$  

•  $\left(x+3\right)\left(x-15\right)$  

•  $-2x^5\left(x+15\right)\left(x-3\right)$  

• Can't Factor 

 Special Case: $x^2-49$ 

• (x - 7)(x - 7)

•  $\left(x-7\right)^2$  

• (x + 7)(x - 7)

• Can't Factor