Question

How do you factor `2x^3 + 2x^2 - 84x`?

Answer 1

`2x(x+7)(x-6)`

Explanation:

The first step is to take out the `color(blue)"common factor"` of 2x

`rArr2x(x^2+x-42) ........ (A)`

Now factorise the `color(blue)"quadratic"` inside the bracket.

Using the a-c method, find the factors of - 42 which sum to +1

These are +7 and - 6

`rArrx^2+x-42=(x+7)(x-6)`

substituting these into (A) gives the factorised form.

`rArr2x^3+2x^2-84x=2x(x+7)(x-6)`

Answer 2

`2x(x^2+x-42)=2x(x-6)(x+7)`

Explanation:

And from this start:

`x^2+x-42=(x-6)(x+7)` (If this were not immediately obvious, I could have used the quadratic equation and solved for `x` in the quadratic.

And thus, `2x^3+2x^2-84x` `=` `2x(x-6)(x+7)`