Question
Multiply polynomial $ \, \color{blue}{ x^2+8x+2 } \, $ by $ \, \color{orangered}{ 2x-7 }$.
Answer
$$ \left( \color{blue}{x^2+8x+2} \right) \cdot \left( \color{orangered}{2x-7} \right) = 2x^3+9x^2-52x-14 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{8x} & \color{blue}{2} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{-7} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{8x} & \color{blue}{2} \\ \hline \color{blue}{2x} & \color{orangered}{2x^3} & \color{orangered}{16x^2} & \color{orangered}{4x} \\ \hline \color{blue}{-7} & \color{orangered}{-7x^2} & \color{orangered}{-56x} & \color{orangered}{-14} \\ \hline \end{darray} $$Combine like terms:
$$ 2x^3 + 16x^2-7x^2 + 4x-56x-14 = \\ 2x^3+9x^2-52x-14 $$This page was created using
Polynomial Operations Calculator