Multiply polynomial $ \, \color{blue}{ x+6 } \, $ by $ \, \color{orangered}{ -5x^2+7x-10 }$.

$$ \left( \color{blue}{x+6} \right) \cdot \left( \color{orangered}{-5x^2+7x-10} \right) = -5x^3-23x^2+32x-60 $$

We can multiply polynomials by using a GRID METHOD

Write one of the polynomials across the top and the other down the left side.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-5x^2} & \color{blue}{7x} & \color{blue}{-10} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{6} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-5x^2} & \color{blue}{7x} & \color{blue}{-10} \\ \hline \color{blue}{x} & \color{orangered}{-5x^3} & \color{orangered}{7x^2} & \color{orangered}{-10x} \\ \hline \color{blue}{6} & \color{orangered}{-30x^2} & \color{orangered}{42x} & \color{orangered}{-60} \\ \hline \end{darray} $$

Combine like terms:

$$ -5x^3 + 7x^2-30x^2-10x + 42x-60 = \\ -5x^3-23x^2+32x-60 $$

Polynomial Operations Calculator