Question
Multiply polynomial $ \, \color{blue}{ 2x-3 } \, $ by $ \, \color{orangered}{ 3x^2-x+6 }$.
Answer
$$ \left( \color{blue}{2x-3} \right) \cdot \left( \color{orangered}{3x^2-x+6} \right) = 6x^3-11x^2+15x-18 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-x} & \color{blue}{6} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{-3} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-x} & \color{blue}{6} \\ \hline \color{blue}{2x} & \color{orangered}{6x^3} & \color{orangered}{-2x^2} & \color{orangered}{12x} \\ \hline \color{blue}{-3} & \color{orangered}{-9x^2} & \color{orangered}{3x} & \color{orangered}{-18} \\ \hline \end{darray} $$Combine like terms:
$$ 6x^3-2x^2-9x^2 + 12x + 3x-18 = \\ 6x^3-11x^2+15x-18 $$This page was created using
Polynomial Operations Calculator