Question
Factor polynomial $$ -x^{4}+5x^{3}-3x+15 $$
Answer
$$ -x^{4}+5x^{3}-3x+15 = -( x^{3}+3 )( x-5 ) $$
Explanation
Step 1 :
After factoring out $ -1 $ we have:
$$ -x^{4}+5x^{3}-3x+15 = - ~ ( x^{4}-5x^{3}+3x-15 ) $$Step 2 :
To factor $ x^{4}-5x^{3}+3x-15 $ we can use factoring by grouping:
Group $ \color{blue}{ x^{4} }$ with $ \color{blue}{ -5x^{3} }$ and $ \color{red}{ 3x }$ with $ \color{red}{ -15 }$ then factor each group.
$$ \begin{aligned} x^{4}-5x^{3}+3x-15 = ( \color{blue}{ x^{4}-5x^{3} } ) + ( \color{red}{ 3x-15 }) &= \\ &= \color{blue}{ x^{3}( x-5 )} + \color{red}{ 3( x-5 ) } = \\ &= (x^{3}+3)(x-5) \end{aligned} $$This page was created using
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