Question
Multiply polynomial $ \, \color{blue}{ 5x^2-x-3 } \, $ by $ \, \color{orangered}{ 2x+6 }$.
Answer
$$ \left( \color{blue}{5x^2-x-3} \right) \cdot \left( \color{orangered}{2x+6} \right) = 10x^3+28x^2-12x-18 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5x^2} & \color{blue}{-x} & \color{blue}{-3} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{6} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5x^2} & \color{blue}{-x} & \color{blue}{-3} \\ \hline \color{blue}{2x} & \color{orangered}{10x^3} & \color{orangered}{-2x^2} & \color{orangered}{-6x} \\ \hline \color{blue}{6} & \color{orangered}{30x^2} & \color{orangered}{-6x} & \color{orangered}{-18} \\ \hline \end{darray} $$Combine like terms:
$$ 10x^3-2x^2 + 30x^2-6x-6x-18 = \\ 10x^3+28x^2-12x-18 $$This page was created using
Polynomial Operations Calculator