One very common process which is necessary in Algebra is factoring quadratics. The ability to factor quadratics gives us the ability to solve many second degree equations.

In this reading, we're going to look at the very simplest kind of quadratic factoring problem: factoring a quadratic with no leading coefficient.

What does that mean? It simply means that the x²term has no number in front of it.

Example 1: Factor x² + 6x + 8.

Solution: There are two very important numbers we need to look at in this problem: +6 and +8. The first step in factoring this expression is to find:

Two numbers that add to +6, and multiply to +8.

___ + ___ = +6

___ x ___ = +8

Have you found them? They are: +2 and +4.

2 + 4 = 6
2 x 4 = 8

Once you've found these two numbers, you pretty much have the answer:

x² + 6x + 8 = (x + 2)(x + 4)

Example 2: Factor x² - 2x - 15

Solution: The two important numbers here are -2 and -15. We want two numbers that add to -2, and multiply to 15.

Did you find them? Hint: one of them is negative!

-5 + 3 = -2
-5 x 3 = -15

So the answer is (x - 5)(x + 3).

Example 3: Factor x² - 8x + 12

Solution: We want two numbers that add to -8, and multiply to +12. In this case, both of the numbers are negative:

-6 + -2 = -8
-6 x -2 = +12

So the answer is (x - 6)(x - 2).