Video Transcript
Factor the expression six 𝑝
squared plus three 𝑝 minus six 𝑝𝑞 completely.
Given the expression six 𝑝
squared plus three 𝑝 minus six 𝑝𝑞, we need to find the highest common
factor. The coefficients of all three
terms are divisible by three. We know that we could then
undistribute a three. For the first term, six 𝑝
squared would be equal to three times two 𝑝 squared. For the second term, if we
remove a factor of three, we’ll be left with 𝑝 because three times 𝑝 equals
three 𝑝. For the third term, we’ll have
three times negative two 𝑝𝑞 because three times negative two 𝑝𝑞 equals
negative six 𝑝𝑞.
However, we haven’t yet removed
the highest common factor. We know this because we see a
factor that still remains in all three terms. All three terms have at least
one factor of 𝑝. Now, we want to undistribute
this factor of 𝑝, that is, a factor of 𝑝 to the first power. To remove a factor of 𝑝 from
the first term, we’ll be left with two 𝑝. Now, the middle term is the
trickiest. To remove a factor of 𝑝, we
need to think 𝑝 to the first power times what equals 𝑝 to the first power. And that would be one. 𝑝 divided by 𝑝 equals
one.
And finally, to remove a factor
of 𝑝 from negative two 𝑝𝑞, we would be left with negative two 𝑞, which means
we have three 𝑝 times two 𝑝 plus one minus two 𝑞 as our factorized
expression. If we wanted to check and see
if this was true, we would redistribute the three 𝑝 across all three terms. Three 𝑝 times two 𝑝 equals
six 𝑝 squared. Three 𝑝 times one equals three
𝑝. And three 𝑝 times negative two
𝑞 equals negative six 𝑝𝑞. This is the expression we
started with, and so we found the factored form. Three 𝑝 times two 𝑝 plus one
minus two 𝑞.
