Solving Quadratic Equations by Factoring - Concept


Solving rational equations is substantially easier with like denominators. When solving rational equations, first multiply every term in the equation by the common denominator so the equation is "cleared" of fractions. Next, use an appropriate technique for solving for the variable.


When you're asked to solve a quadratic equation, what that means is you're trying to find what x values make that equation true. So one way many students choose to go about this is by using factoring techniques.
Before we get into that though, it's important to think about some stuff you already know about zero. There's a important property we have about zero that's called the zero product property. The zero product property says that if a times b is zero then either a=0 or b=0 and that makes sense. Like a product means multiplying and if you have two numbers multiplied together and your answer is zero, then one of those numbers has to be zero.
It's the same idea with quadratic equations. Let me show you what I mean. Let's just say I have the equation that looks like this y=x+4 times x+1. I factored it, that was my factored form. And let's just say instead of y right there I stuck a zero, either because I was trying to solve or because I was trying to find the x intercepts.
Now think about the zero products property. I have this binomial multiplied by that binomial, I have a product and the answer is zero. What that tells me is that x+4=0 or x+1=0. It's like this guy's a, that guy's b. If a times b is zero, then either a=0 or b=0. This is how I solve for x. Subtract 4 from both sides and I'm going to get my solutions x=-4 or x=-1.
This is how you're going to go about solving quadratic equations by factoring. First get it into factored form, set it equal to zero, and then separate your two factors, make each factor equal to zero and solve for x. This is really useful when you're trying to find the x intercepts when you're graphing a parabola.

zero product property factoring