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

Mar 23, 2018

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:

$\left(x + a\right) \left(x + b\right) = {x}^{2} + x \left(a + b\right) + \left(a \times b\right)$

using those relationships:

$a + b = - 3$
$a \times b = - 40$

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:

$5 + \left(- 8\right) = - 3$ <-- equation satisfied
$5 \times - 8 = - 40$ <-- equation satisfied

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

$\left(x + 5\right) \left(x - 8\right)$