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Solving Quadratic Equations by Factoring  Problem 4
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 I have a problem that I want to solve by factoring and there’s a couple of things that are making me nervous. The first thing is that it's not in standard form and the second thing is I have a whole bunch of big coefficients. So I’m hoping there might be a greatest common factor.
Let’s start by writing this guy equal to 0 by subtracting 27 from both sides. This stuff stays the same, then I have 27 is equal to 0. Now I’m going to look for a greatest common factor. Greatest common factor meaning a combination of numbers and letters that multiplies into to all three of these terms.
Well you guys can probably tell that 3 goes into all of these I could either factor out 3 or 3. I’m going to factor out 3 just being really careful with the minus signs. If I factor out 3 like undistributing I’ll have 3 times +6x and times +9 equal to 0.
Now I’m not done factoring yet because this trinomial can be factored even further. 3 times (x plus 3), (x plus 3).
My last step is to use the last product properly but this is one is kind of tricky because I have three things being multiplied together that give me the answer 0. So I could kind of write 3 equal 0 and x plus 3 equals 0 and x plus 3 equals 0, although this is never true right? That means I’m not going to get a solution out of there you don’t even need t worry about the greatest common factor it doesn’t affect my x solutions.
Once I’ve gotten rid of that guy I also notice that the same binomial shows up twice. This is a perfect square trinomial, so that tells me I’m only going to have one answer that answer is going to be x equals 3. The only value that makes this statement true is the value 3. To check you would go back and substitute 3 in here for both Xs and make sure that your answer does indeed give you +27.
When you are doing these problems look for a greatest common factor like this and if it’s just a constant like 3, it’s not going to give you any solution you can just kind of cancel that guy out it doesn’t affect your final solutions here.
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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 16,020 viewsSolve by factoring:
x² + 4x = 0 
Solving Quadratic Equations by Factoring
Problem 2 13,030 viewsSolve by factoring:
x² + 2x = 15 
Solving Quadratic Equations by Factoring
Problem 3 11,717 viewsSolve by factoring:
x² + 6x + 9 = 0 
Solving Quadratic Equations by Factoring
Problem 4 12,096 viewsSolve by factoring:
3x² − 18x = 27 
Solving Quadratic Equations by Factoring
Problem 5 2,164 views 
Solving Quadratic Equations by Factoring
Problem 6 2,160 views 
Solving Quadratic Equations by Factoring
Problem 7 1,872 views 
Solving Quadratic Equations by Factoring
Problem 8 1,803 views 
Solving Quadratic Equations by Factoring
Problem 9 1,799 views 
Solving Quadratic Equations by Factoring
Problem 10 1,830 views 
Solving Quadratic Equations by Factoring
Problem 11 1,657 views 
Solving Quadratic Equations by Factoring
Problem 12 1,839 views 
Solving Quadratic Equations by Factoring
Problem 13 1,668 views 
Solving Quadratic Equations by Factoring
Problem 14 1,944 views 
Solving Quadratic Equations by Factoring
Problem 15 1,652 views 
Solving Quadratic Equations by Factoring
Problem 16 1,017 views 
Solving Quadratic Equations by Factoring
Problem 17 1,007 views 
Solving Quadratic Equations by Factoring
Problem 18 896 views 
Solving Quadratic Equations by Factoring
Problem 19 1,020 views 
Solving Quadratic Equations by Factoring
Problem 20 942 views 
Solving Quadratic Equations by Factoring
Problem 21 984 views 
Solving Quadratic Equations by Factoring
Problem 22 999 views
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