Question

How do you factor `5x^2-x-18`?

Answer 1

`(5x + 9)(x - 2)`

Explanation:

To factor this quadratic expression we need to play with multipliers for `5` (1x5, 5x1) and multipliers for `-18` (1x18, 2x9 3x6, 6x3, 9x2, 19x1) which add to `-1`:

`(5x + 9)(x - 2)`

Answer 2

Use an AC method to find:

`5x^2-x-18 = (5x+9)(x-2)`

Explanation:

Given:

`5x^2-x-18`

Use an AC method:

Look for a pair of factors of `AC=5*18 = 90` which differ by `B=1`

The pair `10, 9` works.

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

`5x^2-x-18 = 5x^2-10x+9x-18`

`color(white)(5x^2-x-18) = (5x^2-10x)+(9x-18)`

`color(white)(5x^2-x-18) = 5x(x-2)+9(x-2)`

`color(white)(5x^2-x-18) = (5x+9)(x-2)`