Question

1. $6v^2 - 75v + 189$

$3(2 - 25 + 6$

1. $20x^3 - 156x^2 - 216x$

Explanation:

Step1: Factor out GCF for problem 2

$6v^2 - 75v + 189 = 3(2v^2 - 25v + 63)$

Step2: Factor quadratic for problem 2

Find two numbers: $-14$ and $-9$ (product $2*63=126$, sum $-25$)
$2v^2 -25v +63 = 2v^2 -14v -9v +63 = 2v(v-7)-9(v-7)=(2v-9)(v-7)$
So $3(2v^2 -25v +63)=3(2v-9)(v-7)$

Step3: Factor out GCF for problem 4

$20x^3 -156x^2 -216x = 4x(5x^2 -39x -54)$

Step4: Factor quadratic for problem 4

Find two numbers: $6$ and $-45$ (product $5*(-54)=-270$, sum $-39$)
$5x^2 -39x -54 = 5x^2 +6x -45x -54 = x(5x+6)-9(5x+6)=(5x+6)(x-9)$
So $4x(5x^2 -39x -54)=4x(5x+6)(x-9)$

Answer:

1. $3(2v-9)(v-7)$
2. $4x(5x+6)(x-9)$