Factor polynomial $$ 6q^{5}-6q^{4}-7q^{3}+7q^{2} $$
Answer
$$ 6q^{5}-6q^{4}-7q^{3}+7q^{2} = q^{2}( 6q^{2}-7 )( q-1 ) $$
Explanation
Step 1 :
After factoring out $ q^{2} $ we have:
$$ 6q^{5}-6q^{4}-7q^{3}+7q^{2} = q^{2} ( 6q^{3}-6q^{2}-7q+7 ) $$Step 2 :
To factor $ 6q^{3}-6q^{2}-7q+7 $ we can use factoring by grouping:
Group $ \color{blue}{ 6x^{3} }$ with $ \color{blue}{ -6x^{2} }$ and $ \color{red}{ -7x }$ with $ \color{red}{ 7 }$ then factor each group.
$$ \begin{aligned} 6q^{3}-6q^{2}-7q+7 = ( \color{blue}{ 6x^{3}-6x^{2} } ) + ( \color{red}{ -7x+7 }) &= \\ &= \color{blue}{ 6x^{2}( x-1 )} + \color{red}{ -7( x-1 ) } = \\ &= (6x^{2}-7)(x-1) \end{aligned} $$This page was created using
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