Question

What is the factorization of the trinomial below?

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

A. 2x(x^2 + 3)(x + 2)
B. -2x(x - 3)(x + 2)
C. -2x(x + 3)(x + 2)
D. -2x(x + 3)(x - 2)

Answer 1

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

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

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

Its D

Answer 2

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.