Question
Multiply polynomial $ \, \color{blue}{ x-3 } \, $ by $ \, \color{orangered}{ x^2-5x+6 }$.
Answer
$$ \left( \color{blue}{x-3} \right) \cdot \left( \color{orangered}{x^2-5x+6} \right) = x^3-8x^2+21x-18 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-5x} & \color{blue}{6} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{-3} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-5x} & \color{blue}{6} \\ \hline \color{blue}{x} & \color{orangered}{x^3} & \color{orangered}{-5x^2} & \color{orangered}{6x} \\ \hline \color{blue}{-3} & \color{orangered}{-3x^2} & \color{orangered}{15x} & \color{orangered}{-18} \\ \hline \end{darray} $$Combine like terms:
$$ x^3-5x^2-3x^2 + 6x + 15x-18 = \\ x^3-8x^2+21x-18 $$This page was created using
Polynomial Operations Calculator