Question

Determine the factors of 3x2 + 10x − 8. (Which is the right answer?)

A. (3x − 8)(x + 1)
B. (3x − 1)(x + 8)
C. (3x − 4)(x + 2)
D. (3x − 2)(x + 4)

Answer 1

`(3x - 2)(x + 4)`

Step-by-step explanation

The given quadratic trinomial is

`3 {x}^(2) + 10x - 8`

Comparing to the general quadratic trinomial:

`a{x}^(2) + bx + c`

We have a=1, b=10 and c=-8

`ac = 3 * - 8 = - 24`

The factors of -24 that adds up to 10 are -2 and 12.

We split the middle term to obtain;

`3 {x}^(2) + 12x - 2x- 8`

Factor;

`3x(x+ 4) - 2(x + 4)`

Factor further;

`(3x - 2)(x + 4)`

The last option is correct.