Question
Factor polynomial $$ 14x^{4}-42x^{3}-6x^{2}+18x $$
Answer
$$ 14x^{4}-42x^{3}-6x^{2}+18x = 2x( 7x^{2}-3 )( x-3 ) $$
Explanation
Step 1 :
After factoring out $ 2x $ we have:
$$ 14x^{4}-42x^{3}-6x^{2}+18x = 2x ( 7x^{3}-21x^{2}-3x+9 ) $$Step 2 :
To factor $ 7x^{3}-21x^{2}-3x+9 $ we can use factoring by grouping:
Group $ \color{blue}{ 7x^{3} }$ with $ \color{blue}{ -21x^{2} }$ and $ \color{red}{ -3x }$ with $ \color{red}{ 9 }$ then factor each group.
$$ \begin{aligned} 7x^{3}-21x^{2}-3x+9 = ( \color{blue}{ 7x^{3}-21x^{2} } ) + ( \color{red}{ -3x+9 }) &= \\ &= \color{blue}{ 7x^{2}( x-3 )} + \color{red}{ -3( x-3 ) } = \\ &= (7x^{2}-3)(x-3) \end{aligned} $$This page was created using
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