Question Video: Determining the Greatest Common Factor of an Algebraic Expression Mathematics • 7th Grade

Video Transcript

Find the highest common factor of the two terms in this expression, four 𝑥 to the fourth power minus 18𝑥 cubed.

Our expression is four 𝑥 to the fourth power minus 18𝑥 cubed. And here are the two terms. We’re trying to find the highest common factor. The first term has a factor of four and a factor of 𝑥 to the fourth power. The second term has a factor of 18 and 𝑥 cubed. But four is not a factor of 18. But we recognize four and 18 are both even numbers, so we know they both have a factor of two. Four is two times two, and 18 is two times nine. So, both have a factor of two.

But now we need to think about how we would deal with this 𝑥 to the fourth power and 𝑥 cubed. We could say that 𝑥 to the fourth power is equal to 𝑥 to the first power times 𝑥 cubed. Then, we see that both of these terms have a factor of 𝑥 cubed. So, we can rewrite four times 𝑥 to the fourth power as two times 𝑥 cubed times two 𝑥. And 18𝑥 cubed can be rewritten as two 𝑥 cubed times nine, which shows that two 𝑥 cubed is the highest common factor of these two terms.