Question

How do you factor `x^2-5x-14`?

Answer 1

`(x+a)(x+b)=x^2+(a+b)x+ab`

So we want two number whose product (multiply) is `-14` and whose sum (add) is `-5`.

To get negative 14 when we multiply, we'll have to have one positive and one negative number. Because we want them to add up to a negative sum, we'll need the bigger number (greater absolute value) to be negative.

List of whole numbers we can multiply to get `14`

`1xx14` won't work because `1+(-14) !=0`

`2xx7` will work: `2xx-7 = -14` and `2+(-7) = -5`

Check:

`(x+2)(x-7)` do we get `x^2-5x-14`?

Yes, so we've factored correctly.