Question
Multiply polynomial $ \, \color{blue}{ -x^2+9 } \, $ by $ \, \color{orangered}{ -3x^2-11x+4 }$.
Answer
$$ \left( \color{blue}{-x^2+9} \right) \cdot \left( \color{orangered}{-3x^2-11x+4} \right) = 3x^4+11x^3-31x^2-99x+36 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-3x^2} & \color{blue}{-11x} & \color{blue}{4} \\ \hline \color{blue}{-x^2} & & & \\ \hline \color{blue}{9} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-3x^2} & \color{blue}{-11x} & \color{blue}{4} \\ \hline \color{blue}{-x^2} & \color{orangered}{3x^4} & \color{orangered}{11x^3} & \color{orangered}{-4x^2} \\ \hline \color{blue}{9} & \color{orangered}{-27x^2} & \color{orangered}{-99x} & \color{orangered}{36} \\ \hline \end{darray} $$Combine like terms:
$$ 3x^4 + 11x^3-27x^2-4x^2-99x + 36 = \\ 3x^4+11x^3-31x^2-99x+36 $$This page was created using
Polynomial Operations Calculator