Question
Multiply polynomial $ \, \color{blue}{ x^2-8x+4 } \, $ by $ \, \color{orangered}{ x-5 }$.
Answer
$$ \left( \color{blue}{x^2-8x+4} \right) \cdot \left( \color{orangered}{x-5} \right) = x^3-13x^2+44x-20 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-8x} & \color{blue}{4} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{-5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-8x} & \color{blue}{4} \\ \hline \color{blue}{x} & \color{orangered}{x^3} & \color{orangered}{-8x^2} & \color{orangered}{4x} \\ \hline \color{blue}{-5} & \color{orangered}{-5x^2} & \color{orangered}{40x} & \color{orangered}{-20} \\ \hline \end{darray} $$Combine like terms:
$$ x^3-8x^2-5x^2 + 4x + 40x-20 = \\ x^3-13x^2+44x-20 $$This page was created using
Polynomial Operations Calculator