Learn math, science, English SAT & ACT from
highquaility study
videos by expert teachers
Learn math, science, English SAT & ACT from
highquaility study videos by expert teachers
Review of the Methods of Factoring  Problem 2
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
Factoring an expression with four terms; whenever you see an expression with four terms, that’s a pretty good sign that you’re going to have to factor by grouping. Remember grouping is you’re grouping a pair and a pair and then hopefully when you factor something out those inside terms you’ll be left with are the same, so you can factor out again.
So let’s look at this. The first thing you always want to do is just group up pairs and you want to group up pairs that have something in common. In this case the first two terms have a 2b². The second have nothing in common that’s okay though because we’re going to see that when we factor this out, we’re actually going to be left with an 8 plus 4 as well.
So what we want to do is factor out a common. Group these two together and factor out the common factor. In this case 2b² leaving us with a minus 4. Then we’re left with minus a plus 4 over here. We want to somehow group these together take something out so that this term and the a minus 4 are the same so we have sort of a bigger term here and a bigger term here that both share a factor.
Right now I see these are equal and opposite which means if I take out a 1, these meet with a, a minus 4. You can always check, distribute back in 1 times a is –a. 1 times 4 is +4. So we’re left with 2b², a minus 4, minus 1, a minus 4. Okay so really we have what I would call two complicated terms. We have a term here and a term here and again what we want to do is take out the common factor. They both have a, a minus 4. So we take out the a minus 4, this term is left with a 2b² and this term with a minus 1.
So what we have done is we’ve grouped it up, made each of our insides to be the same, factored that out and we ended up with this. We could almost factor this second term. It’s almost a difference of squares expect that we have these 2 in here. If this 2 wasn’t here, you’d be able to factor it as b plus 1a and b minus 1, but because we have this 2, it’s not quite a square, it’s not going to be able to be factored.
So in order to factor by grouping, group them together, factor it out, factor out again and you’re done.
Please enter your name.
Are you sure you want to delete this comment?
Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
Concept (1)
Sample Problems (13)
Need help with a problem?
Watch expert teachers solve similar problems.

Review of the Methods of Factoring
Problem 1 9,228 viewsFactor:
2x²(x + 1)² − 7x(x + 1)² + 6(x + 1)² 
Review of the Methods of Factoring
Problem 2 6,395 viewsFactor:
2ab² − 8b² − a + 4 
Review of the Methods of Factoring
Problem 3 5,585 viewsFactor:
16x² − 24xy + 9y² 
Review of the Methods of Factoring
Problem 4 5,137 viewsFactor:
8x³ − 27 
Review of the Methods of Factoring
Problem 5 4,908 viewsFactor:
10x² + 23xy − 5y² 
Review of the Methods of Factoring
Problem 6 316 views 
Review of the Methods of Factoring
Problem 7 322 views 
Review of the Methods of Factoring
Problem 8 320 views 
Review of the Methods of Factoring
Problem 9 275 views 
Review of the Methods of Factoring
Problem 10 226 views 
Review of the Methods of Factoring
Problem 11 269 views 
Review of the Methods of Factoring
Problem 12 253 views 
Review of the Methods of Factoring
Problem 13 292 views
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete