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Solving Quadratic Equations by Factoring  Problem 3
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
Here’s a problem that I want to solve by factoring. What I’m going to be doing is looking for two numbers that multiply to +9 and add up to +6. That’s not too hard I know that’s going to be x plus 3 and x plus 3.
Now this is kind of strange because what I have is x plus 3 squared equal to 0 and I need to set each factor equal to 0 in order to solve for x but both the factors are the same that’s okay. What I have going on here is a problem where I have only one solution. The only solution comes from setting x plus 3 equals 0 because both my factors are the same. What this means is the only number that will make this statement true is the value 3.
Let’s just check and make sure that 3 does indeed work. 3 times itself is 9 plus, 6 times 3 plus 9 if that’s equal to 0 I’m a happy camper. 9 take away 18 plus 9 good, it does indeed equal to 0.
So this is a strange problem because I have only one solution, the way you might recognize this is if you are good at spotting perfect square trinomials. This is a perfect square trinomial because it comes from a binomial times itself. Anytime you have a perfect square trinomial it means you are only going to have one x solution.
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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 15,747 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 11,478 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 1,978 views 
Solving Quadratic Equations by Factoring
Problem 6 1,961 views 
Solving Quadratic Equations by Factoring
Problem 7 1,702 views 
Solving Quadratic Equations by Factoring
Problem 8 1,639 views 
Solving Quadratic Equations by Factoring
Problem 9 1,607 views 
Solving Quadratic Equations by Factoring
Problem 10 1,670 views 
Solving Quadratic Equations by Factoring
Problem 11 1,509 views 
Solving Quadratic Equations by Factoring
Problem 12 1,639 views 
Solving Quadratic Equations by Factoring
Problem 13 1,512 views 
Solving Quadratic Equations by Factoring
Problem 14 1,765 views 
Solving Quadratic Equations by Factoring
Problem 15 1,510 views 
Solving Quadratic Equations by Factoring
Problem 16 882 views 
Solving Quadratic Equations by Factoring
Problem 17 887 views 
Solving Quadratic Equations by Factoring
Problem 18 782 views 
Solving Quadratic Equations by Factoring
Problem 19 850 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 22 849 views
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