Question
Multiply polynomial $ \, \color{blue}{ 4x^2+2x+7 } \, $ by $ \, \color{orangered}{ -x-2 }$.
Answer
$$ \left( \color{blue}{4x^2+2x+7} \right) \cdot \left( \color{orangered}{-x-2} \right) = -4x^3-10x^2-11x-14 $$
Explanation
We can multiply polynomials by using a GRID METHOD
Write one of the polynomials across the top and the other down the left side.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^2} & \color{blue}{2x} & \color{blue}{7} \\ \hline \color{blue}{-x} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^2} & \color{blue}{2x} & \color{blue}{7} \\ \hline \color{blue}{-x} & \color{orangered}{-4x^3} & \color{orangered}{-2x^2} & \color{orangered}{-7x} \\ \hline \color{blue}{-2} & \color{orangered}{-8x^2} & \color{orangered}{-4x} & \color{orangered}{-14} \\ \hline \end{darray} $$Combine like terms:
$$ -4x^3-2x^2-8x^2-7x-4x-14 = \\ -4x^3-10x^2-11x-14 $$This page was created using
Polynomial Operations Calculator