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. Weβre 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.
