Question

Fully factorise

`12x^3 + 38x^2 - 14x`

Answer 1

`2x(3x-1)(2x+7)`

Explanation:

`12x^3+3x^2-14x\\`

Factor out common factor: (2x)

`=2x(6x^2+19x-7)`

Factor
`6x^2+19x-7`

`= 2x(3x-1)(2x+7)`

Hope this helps! :) Sorry for the late reply

Answer 2

2x(2x + 7)(3x - 1).

Explanation:

12x^3 + 38x^2 - 14x

= x(12x^2 + 38x - 14)

= 2x(6x^2 + 19x - 7)

To factor the expression in the parentheses we need 2 numbers whose product is (6 * -7) = - 42 and whose sum = +19.

These are +21 and - 2.

So, we write:

6x^2 - 2x + 21x - 7

= 2x(3x - 1) + 7(3x - 1)

= (2x + 7)(3x - 1)

So, the answer is 2x(2x + 7)(3x - 1).