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Greatest Common Factors  Problem 2
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’m given polynomials and I’m going to look for monomial that’s the greatest common factor. First thing I’m going to look at is the numbers or the constants or the coefficients and then I’m going to be looking at the variable parts. So here we go.
5 and 10, the number that multiplies into both 5 and 10 is 5. So that’s going to be part of my greatest common factor. X to the third and x, the number of Xs that goes into both of those is just 1x. So if I were to be undistributing I need to think 5x multiplied by what gives me 5x to the third. 5x times x² is what gives me 5x to the third.
Here I have my greatest common factor and now I’m kind of thinking backwards. I’m like undistributing. 5x times what gives me 10x? Just 2. There we go, that’s the factor form of this binomial. I took this binomial and wrote it as the product of 2 different other polynomials.
Let’s look at this guy. I want to figure out what number goes into 6, 12 and 60. Well the number that goes into all of those is 6.that’s going to be part of my greatest common factor. Then I want to look at the ps. How many ps go into each of these? It’s got to be one p. Next I want to think 6p times what gives me 6p to the third? There it is. 6p times 2 would give me that, sorry, 6p times 2gives me that 12 part. I still need one more p. Last but not least I want to do 6p times what gives me 60p. That’s going to be 10. I think that’s my factored form, but that’s kind of confusing. I want to show you guys how to check your work and that’s by distributing. So let me just check.
By distributing 6p times p² I have 6p to the third take away 12p² take away 60p. Good, that’s how I know I did it correctly because I went back and distributed. So you guys you can absolutely do these problems. It’s just important that you start by finding the common, greatest common factor and from there you go through the undistributing process. Figure out what do you multiply that greatest common factor by in order to get each of the original common terms.
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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.
Your tutorials are good and you have a personality as well. I hope you have more advanced college level stuff, because I like the way you teach.”
Thanks alot for such great lectures... I never found learning this easier ever before... keep up the great work.... :)”
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Sample Problems (8)
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Greatest Common Factors
Problem 1 10,762 viewsFind the greatest common factor of
a) 24 and 60b) 18x² and 27x³ 
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Problem 2 8,526 viewsFactor:
a) 5x³ + 10xb) 6p³ − 12p² − 60p 
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Problem 3 7,000 viewsFactor:
3x(x + 6) − 10(x + 6) 
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Problem 4 1,034 views 
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Problem 5 988 views 
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Problem 6 966 views 
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Problem 7 903 views 
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Problem 8 550 views
Comments (1)
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micah · 1 month, 3 weeks ago
could you give us more question like this too practice