Question

20 points! Thank you

Answer 1

How to get answer by Mimiwhatsup:

$3x^3+6x^2-24x\\\mathrm{Factor\:out\:common\:term\:}3x:\quad 3x\left(x^2+2x-8\right)\\3x^3+6x^2-24x\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c\\x^2=xx\\x^3=x^2x\\=3x^2x+6xx-24x\\\mathrm{Rewrite\:}24\mathrm{\:as\:}3\cdot \:8\\\mathrm{Rewrite\:}6\mathrm{\:as\:}3\cdot \:2\\=3x^2x+3\cdot \:2xx-3\cdot \:8x\\\mathrm{Factor\:out\:common\:term\:}3x\\=3x\left(x^2+2x-8\right)\\\mathrm{Factor}\:x^2+2x-8:\quad \left(x-2\right)\left(x+4\right)\\x^2+2x-8\\Break\:the\:expression\:into\:groups$

$=\left(x^2-2x\right)+\left(4x-8\right)\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2-2x\mathrm{:\quad }x\left(x-2\right)\\\mathrm{Factor\:out\:}4\mathrm{\:from\:}4x-8\mathrm{:\quad }4\left(x-2\right)\\=x\left(x-2\right)+4\left(x-2\right)\\\mathrm{Factor\:out\:common\:term\:}\left(x-2\right)\\=\left(x-2\right)\left(x+4\right)\\Answer: =3x\left(x-2\right)\left(x+4\right)$

A. Is the correct answer.

Answer 2

$HEY THERE !!$

Factorization of the trinomial
3x^3 +6x^2 -24x
will be :-

taking common 3x

=>3x(x^2+2x-12)......1️⃣

now the factorization of (x^2+2x-12) will be
(x-2)(x+4).......2️⃣

so your answer from 1️⃣and 2️⃣ is (A) 3x(x-2)(x+4).

Hope it helped you.