Question
Multiply polynomial $ \, \color{blue}{ x+4 } \, $ by $ \, \color{orangered}{ 4x^2+3x-2 }$.
Answer
$$ \left( \color{blue}{x+4} \right) \cdot \left( \color{orangered}{4x^2+3x-2} \right) = 4x^3+19x^2+10x-8 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^2} & \color{blue}{3x} & \color{blue}{-2} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{4} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^2} & \color{blue}{3x} & \color{blue}{-2} \\ \hline \color{blue}{x} & \color{orangered}{4x^3} & \color{orangered}{3x^2} & \color{orangered}{-2x} \\ \hline \color{blue}{4} & \color{orangered}{16x^2} & \color{orangered}{12x} & \color{orangered}{-8} \\ \hline \end{darray} $$Combine like terms:
$$ 4x^3 + 3x^2 + 16x^2-2x + 12x-8 = \\ 4x^3+19x^2+10x-8 $$This page was created using
Polynomial Operations Calculator