Question
Multiply polynomial $ \, \color{blue}{ -4x+5 } \, $ by $ \, \color{orangered}{ 3x^2-2x-1 }$.
Answer
$$ \left( \color{blue}{-4x+5} \right) \cdot \left( \color{orangered}{3x^2-2x-1} \right) = -12x^3+23x^2-6x-5 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-2x} & \color{blue}{-1} \\ \hline \color{blue}{-4x} & & & \\ \hline \color{blue}{5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-2x} & \color{blue}{-1} \\ \hline \color{blue}{-4x} & \color{orangered}{-12x^3} & \color{orangered}{8x^2} & \color{orangered}{4x} \\ \hline \color{blue}{5} & \color{orangered}{15x^2} & \color{orangered}{-10x} & \color{orangered}{-5} \\ \hline \end{darray} $$Combine like terms:
$$ -12x^3 + 8x^2 + 15x^2 + 4x-10x-5 = \\ -12x^3+23x^2-6x-5 $$This page was created using
Polynomial Operations Calculator