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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 15,530 viewsSolve by factoring:
x² + 4x = 0 
Solving Quadratic Equations by Factoring
Problem 2 12,596 viewsSolve by factoring:
x² + 2x = 15 
Solving Quadratic Equations by Factoring
Problem 3 11,333 viewsSolve by factoring:
x² + 6x + 9 = 0 
Solving Quadratic Equations by Factoring
Problem 4 11,569 viewsSolve by factoring:
3x² − 18x = 27 
Solving Quadratic Equations by Factoring
Problem 5 1,880 views 
Solving Quadratic Equations by Factoring
Problem 6 1,855 views 
Solving Quadratic Equations by Factoring
Problem 7 1,635 views 
Solving Quadratic Equations by Factoring
Problem 8 1,551 views 
Solving Quadratic Equations by Factoring
Problem 9 1,531 views 
Solving Quadratic Equations by Factoring
Problem 10 1,578 views 
Solving Quadratic Equations by Factoring
Problem 11 1,439 views 
Solving Quadratic Equations by Factoring
Problem 12 1,542 views 
Solving Quadratic Equations by Factoring
Problem 13 1,444 views 
Solving Quadratic Equations by Factoring
Problem 14 1,668 views 
Solving Quadratic Equations by Factoring
Problem 15 1,442 views 
Solving Quadratic Equations by Factoring
Problem 16 795 views 
Solving Quadratic Equations by Factoring
Problem 17 819 views 
Solving Quadratic Equations by Factoring
Problem 18 708 views 
Solving Quadratic Equations by Factoring
Problem 19 758 views 
Solving Quadratic Equations by Factoring
Problem 20 748 views 
Solving Quadratic Equations by Factoring
Problem 21 760 views 
Solving Quadratic Equations by Factoring
Problem 22 767 views
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