Question

How do you factor the trinomial `x² + 8x - 20`?

Answer 1

`x^2+8x-20 = (x+10)(x-2)`

Explanation:

Here are a couple of methods...

Fishing for factors

Given:

`x^2+8x-20`

Notice the negative constant term. Hence look for a pair of factors of `20` whose difference is `8`.

The pair `10, 2` works in that `10 * 2 = 20` and `10 - 2 = 8`

Hence we find:

`x^2+8x-20 = (x+10)(x-2)`

Completing the square

Complete the square, then use the difference of squares identity:

`A^2-B^2 = (A-B)(A+B)`

with `A=(x+4)` and `B=6` as follows:

`x^2+8x-20 = x^2+2(x)(4)+4^2-4^2-20`

`color(white)(x^2+8x-20) = x^2+2(x)(4)+4^2-36`

`color(white)(x^2+8x-20) = (x+4)^2-6^2`

`color(white)(x^2+8x-20) = ((x+4)-6)((x+4)+6)`

`color(white)(x^2+8x-20) = (x-2)(x+10)`