Question
Multiply polynomial $ \, \color{blue}{ 3x+4 } \, $ by $ \, \color{orangered}{ 2x^2-3x-7 }$.
Answer
$$ \left( \color{blue}{3x+4} \right) \cdot \left( \color{orangered}{2x^2-3x-7} \right) = 6x^3-x^2-33x-28 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{-3x} & \color{blue}{-7} \\ \hline \color{blue}{3x} & & & \\ \hline \color{blue}{4} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{-3x} & \color{blue}{-7} \\ \hline \color{blue}{3x} & \color{orangered}{6x^3} & \color{orangered}{-9x^2} & \color{orangered}{-21x} \\ \hline \color{blue}{4} & \color{orangered}{8x^2} & \color{orangered}{-12x} & \color{orangered}{-28} \\ \hline \end{darray} $$Combine like terms:
$$ 6x^3-9x^2 + 8x^2-21x-12x-28 = \\ 6x^3-x^2-33x-28 $$This page was created using
Polynomial Operations Calculator