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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 15,315 viewsSolve by factoring:
x² + 4x = 0 
Solving Quadratic Equations by Factoring
Problem 2 12,412 viewsSolve by factoring:
x² + 2x = 15 
Solving Quadratic Equations by Factoring
Problem 3 11,180 viewsSolve by factoring:
x² + 6x + 9 = 0 
Solving Quadratic Equations by Factoring
Problem 4 11,336 viewsSolve by factoring:
3x² − 18x = 27 
Solving Quadratic Equations by Factoring
Problem 5 1,768 views 
Solving Quadratic Equations by Factoring
Problem 6 1,738 views 
Solving Quadratic Equations by Factoring
Problem 7 1,513 views 
Solving Quadratic Equations by Factoring
Problem 8 1,442 views 
Solving Quadratic Equations by Factoring
Problem 9 1,432 views 
Solving Quadratic Equations by Factoring
Problem 10 1,472 views 
Solving Quadratic Equations by Factoring
Problem 11 1,334 views 
Solving Quadratic Equations by Factoring
Problem 12 1,416 views 
Solving Quadratic Equations by Factoring
Problem 13 1,341 views 
Solving Quadratic Equations by Factoring
Problem 14 1,536 views 
Solving Quadratic Equations by Factoring
Problem 15 1,333 views 
Solving Quadratic Equations by Factoring
Problem 16 692 views 
Solving Quadratic Equations by Factoring
Problem 17 713 views 
Solving Quadratic Equations by Factoring
Problem 18 608 views 
Solving Quadratic Equations by Factoring
Problem 19 659 views 
Solving Quadratic Equations by Factoring
Problem 20 654 views 
Solving Quadratic Equations by Factoring
Problem 21 661 views 
Solving Quadratic Equations by Factoring
Problem 22 652 views
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