Question
Multiply polynomial $ \, \color{blue}{ 3x^2+4x-5 } \, $ by $ \, \color{orangered}{ 3x-1 }$.
Answer
$$ \left( \color{blue}{3x^2+4x-5} \right) \cdot \left( \color{orangered}{3x-1} \right) = 9x^3+9x^2-19x+5 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{4x} & \color{blue}{-5} \\ \hline \color{blue}{3x} & & & \\ \hline \color{blue}{-1} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{4x} & \color{blue}{-5} \\ \hline \color{blue}{3x} & \color{orangered}{9x^3} & \color{orangered}{12x^2} & \color{orangered}{-15x} \\ \hline \color{blue}{-1} & \color{orangered}{-3x^2} & \color{orangered}{-4x} & \color{orangered}{5} \\ \hline \end{darray} $$Combine like terms:
$$ 9x^3 + 12x^2-3x^2-15x-4x + 5 = \\ 9x^3+9x^2-19x+5 $$This page was created using
Polynomial Operations Calculator