Question
Multiply polynomial $ \, \color{blue}{ 5x^2+x-7 } \, $ by $ \, \color{orangered}{ x+5 }$.
Answer
$$ \left( \color{blue}{5x^2+x-7} \right) \cdot \left( \color{orangered}{x+5} \right) = 5x^3+26x^2-2x-35 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5x^2} & \color{blue}{x} & \color{blue}{-7} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5x^2} & \color{blue}{x} & \color{blue}{-7} \\ \hline \color{blue}{x} & \color{orangered}{5x^3} & \color{orangered}{x^2} & \color{orangered}{-7x} \\ \hline \color{blue}{5} & \color{orangered}{25x^2} & \color{orangered}{5x} & \color{orangered}{-35} \\ \hline \end{darray} $$Combine like terms:
$$ 5x^3 + x^2 + 25x^2-7x + 5x-35 = \\ 5x^3+26x^2-2x-35 $$This page was created using
Polynomial Operations Calculator