Question

How do you factor the trinomial `20x^2-13x-15`?

Answer 1

`20x^2-13x-15=(5x+3)(4x-5)`

Explanation:

Use an AC method:

Find a pair of factors of `AC=20*15=300` which differ by `B=13`.

Since `300` is divisible by `5^2` and `13` is not divisible by `5`, one of the factors must be divisible by `25` in order that the other is not divisible by `5`.

With this condition in mind, we quickly find the pair `25, 12` works in that `25*12 = 300` and `25-12 = 13`

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

`20x^2-13x-15`

`=20x^2-25x+12x-15`

`=(20x^2-25x)+(12x-15)`

`=5x(4x-5)+3(4x-5)`

`=(5x+3)(4x-5)`