Question

How do you factor `y= x^2 – 3x – 40` ?

Answer 1

It factors to (x+5)(x-8)

Explanation:

Because we see that the highest order of `x` is 2, and the `x^2` term has no constants, we can write the factored equation as such:

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

using those relationships:

`a+b=-3`
`axxb=-40`

Because the product of `a` and `b` is negative, we know that only one of those terms is negative. The next step is to figure out what combination gives that product and that sum.

I guessed that the numbers must be 5 and -8 because:

`5+(-8)=-3` <-- equation satisfied
`5xx-8=-40` <-- equation satisfied

Now that we have our factors, we can finish our factoring:

`(x+5)(x-8)`