Question
Multiply polynomial $ \, \color{blue}{ x-4 } \, $ by $ \, \color{orangered}{ x^2+x-6 }$.
Answer
$$ \left( \color{blue}{x-4} \right) \cdot \left( \color{orangered}{x^2+x-6} \right) = x^3-3x^2-10x+24 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{x} & \color{blue}{-6} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{-4} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{x} & \color{blue}{-6} \\ \hline \color{blue}{x} & \color{orangered}{x^3} & \color{orangered}{x^2} & \color{orangered}{-6x} \\ \hline \color{blue}{-4} & \color{orangered}{-4x^2} & \color{orangered}{-4x} & \color{orangered}{24} \\ \hline \end{darray} $$Combine like terms:
$$ x^3 + x^2-4x^2-6x-4x + 24 = \\ x^3-3x^2-10x+24 $$This page was created using
Polynomial Operations Calculator