Question
Multiply polynomial $ \, \color{blue}{ x+3 } \, $ by $ \, \color{orangered}{ 3x^2+7x-5 }$.
Answer
$$ \left( \color{blue}{x+3} \right) \cdot \left( \color{orangered}{3x^2+7x-5} \right) = 3x^3+16x^2+16x-15 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{7x} & \color{blue}{-5} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{3} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{7x} & \color{blue}{-5} \\ \hline \color{blue}{x} & \color{orangered}{3x^3} & \color{orangered}{7x^2} & \color{orangered}{-5x} \\ \hline \color{blue}{3} & \color{orangered}{9x^2} & \color{orangered}{21x} & \color{orangered}{-15} \\ \hline \end{darray} $$Combine like terms:
$$ 3x^3 + 7x^2 + 9x^2-5x + 21x-15 = \\ 3x^3+16x^2+16x-15 $$This page was created using
Polynomial Operations Calculator