Factoring polynomials: common binomial factor
About this video
Sal factors n(n - 1) + 3(n - 1) by noticing that both terms share the binomial factor (n - 1). Factoring it out (undistributing) gives (n - 1)(n + 3), which he checks by distributing back.
You'll be able to
- spot a common binomial factor in two terms.
- factor out a common binomial to write a product of two binomials.
- check a factorisation by distributing.
Key words
- binomial
- An expression with two terms, like n - 1 or n + 3.
- factor out
- Pull a common factor out of every term, the reverse of distributing.
- common factor
- Something that both terms are multiplied by.
Transcript
- Whereas to factor the polynomial below as the product of two binomials and we have n times n minus one plus 3 times n minus one. So I encourage you to pause this video and see if you can figure this out. Well, the key is to realizing that both of these terms have n minus one as a factor.
Let me just rewrite the whole thing so we can work on it down here. So this is n times n minus one plus 3 times n minus one. And notice both of them have an n minus one, have an n minus one as a factor. So what we can do is factor out the n minus one or you can view it as undistributing the n minus one and if we do that, we're gonna factor out the n minus one and what are we going to have left over?
Well if you take out the n minus one here if you undistribute it out, you're just going to be left with that n. So you're going to have an n there and then for this second term, you factor this n minus one out. You're just going to be left with this positive three plus three.
And just like that we are done. We have factored the polynomial below as a product of two binomials. So this is the same thing as n minus one times n plus three. And once again you can check this. You can take this n minus one and distribute it. n minus one times n is this term right over here n times n minus one and then n minus one times three is this term right over here.
n minus one times three or three times n minus one.
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