Question
Multiply polynomial $ \, \color{blue}{ x^2-12x+29 } \, $ by $ \, \color{orangered}{ x-4 }$.
Answer
$$ \left( \color{blue}{x^2-12x+29} \right) \cdot \left( \color{orangered}{x-4} \right) = x^3-16x^2+77x-116 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-12x} & \color{blue}{29} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{-4} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-12x} & \color{blue}{29} \\ \hline \color{blue}{x} & \color{orangered}{x^3} & \color{orangered}{-12x^2} & \color{orangered}{29x} \\ \hline \color{blue}{-4} & \color{orangered}{-4x^2} & \color{orangered}{48x} & \color{orangered}{-116} \\ \hline \end{darray} $$Combine like terms:
$$ x^3-12x^2-4x^2 + 29x + 48x-116 = \\ x^3-16x^2+77x-116 $$This page was created using
Polynomial Operations Calculator