Question

AC method

-6p^2-21pq-9q^2

Answer 1

first factor out a -3 so:\[-3(2p^2+7pq+3q^2)\]
now are there any factors of 2*3=6 that add up to the middle term?
yes 6 and 1
so rewite the middle term as 6pq+pq
so\[-3(2p^2+6pq+pq+3q^2)\]
now factor the part in the parentheses by grouping so:
so:\[ -3(2p(p+3q)+q(p+3q))\]

(i factored them by finding the GCF of the terms that are next to each other
so the GCF of :
1.2p^2 and 6pq is 2p
2. pq and 3q^2 is q
thats where the 2p and q come from in the previous equation)

as you can see p+3q is a common factor
so you can write it as:
\[-3[(p+3q)(2p+q)]\]
thats the answer