Question
Factor polynomial $$ 3p^{2}q-30p^{2}+24pq-240p $$
Answer
$$ 3p^{2}q-30p^{2}+24pq-240p = 3p(p+8)(q-10) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ 3p } $:
$$ 3p^2q-30p^2+24pq-240p = 3p ( pq-10p+8q-80 ) $$Step 2 :
To factor $ pq-10p+8q-80 $ we can use factoring by grouping.
Group $ \color{blue}{ pq }$ with $ \color{blue}{ -10p }$ and $ \color{red}{ 8q }$ with $ \color{red}{ -80 }$ then factor each group.
$$ \begin{aligned} pq-10p+8q-80 &= ( \color{blue}{ pq-10p } ) + ( \color{red}{ 8q-80 }) = \\ &= \color{blue}{ p( q-10 )} + \color{red}{ 8( q-10 ) } = \\ &= (p+8)(q-10) \end{aligned} $$This page was created using
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