Factor polynomial $$ 25y^{4}+5y^{3}+30y^{2}+6y $$
Answer
$$ 25y^{4}+5y^{3}+30y^{2}+6y = y( 5y^{2}+6 )( 5y+1 ) $$
Explanation
Step 1 :
After factoring out $ y $ we have:
$$ 25y^{4}+5y^{3}+30y^{2}+6y = y ( 25y^{3}+5y^{2}+30y+6 ) $$Step 2 :
To factor $ 25y^{3}+5y^{2}+30y+6 $ we can use factoring by grouping:
Group $ \color{blue}{ 25x^{3} }$ with $ \color{blue}{ 5x^{2} }$ and $ \color{red}{ 30x }$ with $ \color{red}{ 6 }$ then factor each group.
$$ \begin{aligned} 25y^{3}+5y^{2}+30y+6 = ( \color{blue}{ 25x^{3}+5x^{2} } ) + ( \color{red}{ 30x+6 }) &= \\ &= \color{blue}{ 5x^{2}( 5x+1 )} + \color{red}{ 6( 5x+1 ) } = \\ &= (5x^{2}+6)(5x+1) \end{aligned} $$This page was created using
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