Question

How do you factor `32x^2 + 8x - 12`?

Answer 1

`(8x - 4) * (4x + 3)`

Explanation:

For simplicity write `32x^2 + 8x - 12` as `4*(8x^2 + 2x - 3)`
Now let us try to factorize `(8x^2 + 2x - 3)`
Find two numbers, whose product is equal to the product of the coefficient of `x^2` and the constant AND whose sum is equal to the coefficient of x
In this case, the coefficient of `x^2` is 8 and the constant is -3
and the coefficient of x is 2
So, we should find two numbers whose product is -24 (= 8 * (-3))
and sum is 2
We can easily see that the numbers are 6 & -4
So we can write `(8x^2 + 2x - 3)` as `(8x^2 + 6x - 4x - 3)`

= `2x*(4x + 3) - 1 *(4x + 3)`

= `(2x - 1)*(4x + 3)`

So the original problem is `4 * (2x - 1)*(4x + 3)`

which simplifies to `(8x - 4) * (4x + 3)`