Question

How do you solve `x^2-13x-30` ?

Answer 1

`x^2-13x-30 = (x-15)(x+2)`

Explanation:

I am not sure whether you want to find the zeros or factor the quadratic. Actually these two tasks are quite similar.

We want to find two numbers which multiply to give `30` and whose difference is `13`.

The numbers `15, 2` work in that `15 * 2 = 30` and `15 - 2 = 13`.

Hence we find:

`x^2-13x-30 = (x-15)(x+2)`

This has zeros `x=15` and `x=-2`

Answer 2

Let's see... if you meant to factor this expression, then there is an answer.

We have: `x^2-13x-30`

We ask ourselves: What pair of two factors of `-30` add up to `-13`?

Let's list the possible factors of `-30`.

`-1,30`
`-2,15`
`-3,10`
`-5,6`
`1,-30`
`2,-15`
`3,-10`
`5,-6`

We see that `2,-15` add up to `-13` and have the product of `-30`.

Therefore, we can now factor `x^2-13x-30`.

Using`2,-15` we have:

`(x+2)(x-15)`