Question
Factor polynomial $$ 2x^{6}+3x^{4}+12x^{2}+18 $$
Answer
$$ 2x^{6}+3x^{4}+12x^{2}+18 = ( x^{4}+6 )( 2x^{2}+3 ) $$
Explanation
To factor $ 2x^{6}+3x^{4}+12x^{2}+18 $ we can use factoring by grouping:
Group $ \color{blue}{ 2x^{6} }$ with $ \color{blue}{ 3x^{4} }$ and $ \color{red}{ 12x^{2} }$ with $ \color{red}{ 18 }$ then factor each group.
$$ \begin{aligned} 2x^{6}+3x^{4}+12x^{2}+18 = ( \color{blue}{ 2x^{6}+3x^{4} } ) + ( \color{red}{ 12x^{2}+18 }) &= \\ &= \color{blue}{ x^{4}( 2x^{2}+3 )} + \color{red}{ 6( 2x^{2}+3 ) } = \\ &= (x^{4}+6)(2x^{2}+3) \end{aligned} $$This page was created using
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