Question
Multiply polynomial $ \, \color{blue}{ x^2-5x } \, $ by $ \, \color{orangered}{ x^2+10x+17 }$.
Answer
$$ \left( \color{blue}{x^2-5x} \right) \cdot \left( \color{orangered}{x^2+10x+17} \right) = x^4+5x^3-33x^2-85x $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{10x} & \color{blue}{17} \\ \hline \color{blue}{x^2} & & & \\ \hline \color{blue}{-5x} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{10x} & \color{blue}{17} \\ \hline \color{blue}{x^2} & \color{orangered}{x^4} & \color{orangered}{10x^3} & \color{orangered}{17x^2} \\ \hline \color{blue}{-5x} & \color{orangered}{-5x^3} & \color{orangered}{-50x^2} & \color{orangered}{-85x} \\ \hline \end{darray} $$Combine like terms:
$$ x^4 + 10x^3-5x^3 + 17x^2-50x^2-85x = \\ x^4+5x^3-33x^2-85x $$This page was created using
Polynomial Operations Calculator