# How do you factor and solve #x^2+8x+15=0#?

##### 2 Answers

Find roots that when added come to the middle term coefficient and when multiplied come to the last term and you'll find that

#### Explanation:

The key to factoring these kind of quadratic equations is to find 2 roots that when added up equal the coefficient of the middle term and when multiplied equal the last term.

If I'm having problems finding it, I often list out the factors of the last term and see what adds up to the middle term, like this:

(when things get complicated with negative signs and coefficients in front of the first term, this method can really help keep things organized).

Ok - we know the roots are 3 and 5:

The reason we set the left side equal to 0 is because it's easy to multiply by 0 in one term and get 0 as the overall answer. So what we do now is find out what it'll take to make x+3 = 0 and what it'll take x+5 = 0.

Let's do the x+3 first:

Now the x+5 term:

And those are your answers.

#### Explanation:

Since

And since