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Solving Quadratic Equations by Factoring  Concept
Alissa Fong
Alissa Fong
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
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.
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Alissa Fong
M.A. in Secondary Mathematics, Stanford University
B.S., Stanford University
Alissa has a quirky sense of humor and a relatable personality that make it easy for students to pay attention and understand the material. She has all the math tips and tricks students are looking for.
Sample Problems (22)
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Solving Quadratic Equations by Factoring
Problem 1 15,751 viewsSolve by factoring:
x² + 4x = 0 
Solving Quadratic Equations by Factoring
Problem 2 12,751 viewsSolve by factoring:
x² + 2x = 15 
Solving Quadratic Equations by Factoring
Problem 3 11,480 viewsSolve by factoring:
x² + 6x + 9 = 0 
Solving Quadratic Equations by Factoring
Problem 4 11,782 viewsSolve by factoring:
3x² − 18x = 27 
Solving Quadratic Equations by Factoring
Problem 5 1,979 views 
Solving Quadratic Equations by Factoring
Problem 6 1,962 views 
Solving Quadratic Equations by Factoring
Problem 7 1,705 views 
Solving Quadratic Equations by Factoring
Problem 8 1,640 views 
Solving Quadratic Equations by Factoring
Problem 9 1,610 views 
Solving Quadratic Equations by Factoring
Problem 10 1,672 views 
Solving Quadratic Equations by Factoring
Problem 11 1,511 views 
Solving Quadratic Equations by Factoring
Problem 12 1,642 views 
Solving Quadratic Equations by Factoring
Problem 13 1,512 views 
Solving Quadratic Equations by Factoring
Problem 14 1,767 views 
Solving Quadratic Equations by Factoring
Problem 15 1,511 views 
Solving Quadratic Equations by Factoring
Problem 16 884 views 
Solving Quadratic Equations by Factoring
Problem 17 888 views 
Solving Quadratic Equations by Factoring
Problem 18 783 views 
Solving Quadratic Equations by Factoring
Problem 19 851 views 
Solving Quadratic Equations by Factoring
Problem 20 814 views 
Solving Quadratic Equations by Factoring
Problem 21 846 views 
Solving Quadratic Equations by Factoring
Problem 22 850 views
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