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