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.
