Video: Determining the Greatest Common Factor of an Algebraic Expression

Find the highest common factor of the two terms in this expression, 4π‘₯⁴ βˆ’ 18π‘₯Β³.

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Video Transcript

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

Our expression is four π‘₯ to the fourth power minus 18π‘₯ 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 π‘₯ to the fourth power. The second term has a factor of 18 and π‘₯ 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 π‘₯ to the fourth power and π‘₯ cubed. We could say that π‘₯ to the fourth power is equal to π‘₯ to the first power times π‘₯ cubed. Then, we see that both of these terms have a factor of π‘₯ cubed. So, we can rewrite four times π‘₯ to the fourth power as two times π‘₯ cubed times two π‘₯. And 18π‘₯ cubed can be rewritten as two π‘₯ cubed times nine, which shows that two π‘₯ cubed is the highest common factor of these two terms.

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