Question

Factor the given polynomial completely and match your result to the correct answer below.18m³ +24m²-24mSelect one:O a. 6m(m-4)(3m + 1)O b. 6m(3m2 +6m-4)O c.6m(m+2)(3m-2)O d. The polynomial is prime.

Answer 1

Given:

$18m^^3+24m^2-24m$

Required:

We need to factorize the given polynomial completely.

Explanation:

Take out the common multiple 6m.

$18m^3+24m^2-24m=6m(3m^2+4m-4)$$Use\text{ 4m=6m-2m.}$

$18m^3+24m^2-24m=6m(3m^2+6m-2m-4)$

Take out the common multiple.

$18m^3+24m^2-24m=6m(3m(m+2)-2(m+2))$$18m^3+24m^2-24m=6m(m+2)(3m-2)$

Final answer:

$6m(m+2)(3m-2)$