Question
Multiply polynomial $ \, \color{blue}{ 2x^2-3 } \, $ by $ \, \color{orangered}{ x^2+5x-1 }$.
Answer
$$ \left( \color{blue}{2x^2-3} \right) \cdot \left( \color{orangered}{x^2+5x-1} \right) = 2x^4+10x^3-5x^2-15x+3 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{5x} & \color{blue}{-1} \\ \hline \color{blue}{2x^2} & & & \\ \hline \color{blue}{-3} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{5x} & \color{blue}{-1} \\ \hline \color{blue}{2x^2} & \color{orangered}{2x^4} & \color{orangered}{10x^3} & \color{orangered}{-2x^2} \\ \hline \color{blue}{-3} & \color{orangered}{-3x^2} & \color{orangered}{-15x} & \color{orangered}{3} \\ \hline \end{darray} $$Combine like terms:
$$ 2x^4 + 10x^3-3x^2-2x^2-15x + 3 = \\ 2x^4+10x^3-5x^2-15x+3 $$This page was created using
Polynomial Operations Calculator