Question

How do you factor `12x ^ { 2} - 43x + 36`?

Answer 1

Use an AC method to find:

`12x^2-43x+36 = (4x-9)(3x-4)`

Explanation:

Given:

`12x^2-43x+36`

Use an AC method:

Look for a pair of factors of `AC = 12*36 = 432` with sum `B=43`.

Note that since `43` is odd, it is the sum of an odd and an even number. So one of the factors must contain all of the `2`'s, that is: it must be a multiple of `16`. Note that `16+27 = 43` and `16*27=432`.

So the pair we need is `16, 27`.

Use this pair to split the middle term and factor by grouping:

`12x^2-43x+36 = 12x^2-16x-27x+36`

`color(white)(12x^2-43x+36) = (12x^2-16x)-(27x-36)`

`color(white)(12x^2-43x+36) = 4x(3x-4)-9(3x-4)`

`color(white)(12x^2-43x+36) = (4x-9)(3x-4)`