Question

What does 13m2n3p + 21mp2 equal when completely factored?
(A)13mp(mn3 + 2p)
(B)m2p2(13n3 + 21)
(C)mp(13mn3 + 21p)
(D)mnp(13mn2 + 21p)

Answer 1

first we can start with constants. 13 is prime and doesn't go into 21 so there are no constants to factor out.
Next is the m variable. There are 2 (m*m=m^2) in the first part and 1 in the second, so we can take out 1 m.
Now we have m(13m*n^2*p+21*p^2)
Next we check the n variable. There are 2 in the first part and none in the second, so we can't take any n's out.
Finally, we have the p variable. There is 1 in the first part and 2 in the second so we can take out 1, leaving us with
\[m p (13n ^{2}+21p)\]