Question
Multiply polynomial $ \, \color{blue}{ 2x-3 } \, $ by $ \, \color{orangered}{ x^2-4x+2 }$.
Answer
$$ \left( \color{blue}{2x-3} \right) \cdot \left( \color{orangered}{x^2-4x+2} \right) = 2x^3-11x^2+16x-6 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-4x} & \color{blue}{2} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{-3} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-4x} & \color{blue}{2} \\ \hline \color{blue}{2x} & \color{orangered}{2x^3} & \color{orangered}{-8x^2} & \color{orangered}{4x} \\ \hline \color{blue}{-3} & \color{orangered}{-3x^2} & \color{orangered}{12x} & \color{orangered}{-6} \\ \hline \end{darray} $$Combine like terms:
$$ 2x^3-8x^2-3x^2 + 4x + 12x-6 = \\ 2x^3-11x^2+16x-6 $$This page was created using
Polynomial Operations Calculator