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