Question

How do you factor the trinomial `6x^2-17x+12`?

Answer 1

`6x^2-17x+12 = (3x-4)(2x-3)`

Explanation:

Given:

`6x^2-17x+12`

Use an AC method:

Look for a pair of factors of `AC=6*12=72` with sum `B=17`

The pair `9, 8` works, in that `9*8=72` and `9+8=17`

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

`6x^2-17x+12 = 6x^2-9x-8x+12`

`color(white)(6x^2-17x+12) = (6x^2-9x)-(8x-12)`

`color(white)(6x^2-17x+12) = 3x(2x-3)-4(2x-3)`

`color(white)(6x^2-17x+12) = (3x-4)(2x-3)`