Question
Multiply polynomial $ \, \color{blue}{ 2x^3+18x^2+48x+40 } \, $ by $ \, \color{orangered}{ -x^2 }$.
Answer
$$ \left( \color{blue}{2x^3+18x^2+48x+40} \right) \cdot \left( \color{orangered}{-x^2} \right) = -2x^5-18x^4-48x^3-40x^2 $$
Explanation
We can use distribution property to multiply the polynomial by the monomial.
$$ \begin{aligned} \left( 2x^3+18x^2+48x+40 \right) \cdot \left( \color{orangered}{-x^2} \right) &= 2x^3 \cdot \color{orangered}{-x^2} + 18x^2 \cdot \color{orangered}{-x^2} + 48x \cdot \color{orangered}{-x^2} + 40 \cdot \color{orangered}{-x^2} = \\ &= -2x^5-18x^4-48x^3-40x^2 \end{aligned} $$This page was created using
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