Solving Quadratic Equations by Factoring

You can solve quadratic equations by factoring and then using the Zero-Product Property. Let’s look at an example on how this is done.

Suppose you want to solve x² + 7x + 10 = 0 for x. Make sure that when you are solving quadratic equations by factoring you set the quadratic equal to zero. Next, factor the quadratic.

x² + 7x + 10 = (x + 5)(x + 2)

We can then rewrite our initial equation to read:

(x + 5)(x + 2) = 0

Using the Zero-Product Property we know that either x + 5 = 0 or x + 2 = 0 in order for our equation to equal zero. We can now solve these two equations:

x + 5 = 0
x = -5

or

x + 2 = 0
x = -2

We have now calculated the solution to our quadratic. It is the set {-5, -2}.

Next: Section E, page 6

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