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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 16,012 viewsSolve by factoring:
x² + 4x = 0 
Solving Quadratic Equations by Factoring
Problem 2 13,017 viewsSolve by factoring:
x² + 2x = 15 
Solving Quadratic Equations by Factoring
Problem 3 11,710 viewsSolve by factoring:
x² + 6x + 9 = 0 
Solving Quadratic Equations by Factoring
Problem 4 12,088 viewsSolve by factoring:
3x² − 18x = 27 
Solving Quadratic Equations by Factoring
Problem 5 2,154 views 
Solving Quadratic Equations by Factoring
Problem 6 2,152 views 
Solving Quadratic Equations by Factoring
Problem 7 1,866 views 
Solving Quadratic Equations by Factoring
Problem 8 1,795 views 
Solving Quadratic Equations by Factoring
Problem 9 1,792 views 
Solving Quadratic Equations by Factoring
Problem 10 1,825 views 
Solving Quadratic Equations by Factoring
Problem 11 1,652 views 
Solving Quadratic Equations by Factoring
Problem 12 1,831 views 
Solving Quadratic Equations by Factoring
Problem 13 1,662 views 
Solving Quadratic Equations by Factoring
Problem 14 1,933 views 
Solving Quadratic Equations by Factoring
Problem 15 1,644 views 
Solving Quadratic Equations by Factoring
Problem 16 1,014 views 
Solving Quadratic Equations by Factoring
Problem 17 1,004 views 
Solving Quadratic Equations by Factoring
Problem 18 888 views 
Solving Quadratic Equations by Factoring
Problem 19 1,014 views 
Solving Quadratic Equations by Factoring
Problem 20 938 views 
Solving Quadratic Equations by Factoring
Problem 21 977 views 
Solving Quadratic Equations by Factoring
Problem 22 991 views
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