Question

What is the factorization of the trinomial below?

Answer 1

Answer:  the correct option is

(D) $-2x(x+3)(x-2).$

Step-by-step explanation:  We are given to find the factorization of the following trinomial :

$T=-2x^3-2x^2+12x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

The factorization of the given trinomial (i) is as follows :

$T\\\\=-2x^3-2x^2+12x\\\\=-2x(x^2+x-6)\\\\=-2x(x^2+3x-2x-6)~~~~~~~~~~[\textup{the sum of 3 and -2 is 1 and product is -6}]\\\\=-2x(x(x+3)-2(x+3))\\\\=-2x(x+3)(x-2).$

Thus, the required factorization of the given trinomial is $-2x(x+3)(x-2).$

Option (D) is CORRECT.

Answer 2

-2x^3 - 2x^2 + 12x

= -2x (x^2 + x - 6)

= -2x(x + 3)(x - 2)

Its D