Question
Multiply polynomial $ \, \color{blue}{ 3x^3+2x-3 } \, $ by $ \, \color{orangered}{ 5x+6 }$.
Answer
$$ \left( \color{blue}{3x^3+2x-3} \right) \cdot \left( \color{orangered}{5x+6} \right) = 15x^4+18x^3+10x^2-3x-18 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^3} & \color{blue}{2x} & \color{blue}{-3} \\ \hline \color{blue}{5x} & & & \\ \hline \color{blue}{6} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^3} & \color{blue}{2x} & \color{blue}{-3} \\ \hline \color{blue}{5x} & \color{orangered}{15x^4} & \color{orangered}{10x^2} & \color{orangered}{-15x} \\ \hline \color{blue}{6} & \color{orangered}{18x^3} & \color{orangered}{12x} & \color{orangered}{-18} \\ \hline \end{darray} $$Combine like terms:
$$ 15x^4 + 10x^2 + 18x^3-15x + 12x-18 = \\ 15x^4+18x^3+10x^2-3x-18 $$This page was created using
Polynomial Operations Calculator