Step 1: First we have to write polynomials in descending order.

$$ \begin{aligned} P(x) &= -9x^2+3x-6 \\ Q(x) &= 2x+5 \\ \end{aligned} $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-9x^2} & \color{blue}{3x} & \color{blue}{-6} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{5} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-9x^2} & \color{blue}{3x} & \color{blue}{-6} \\ \hline \color{blue}{2x} & \color{orangered}{-18x^3} & \color{orangered}{6x^2} & \color{orangered}{-12x} \\ \hline \color{blue}{5} & \color{orangered}{-45x^2} & \color{orangered}{15x} & \color{orangered}{-30} \\ \hline \end{darray} $$

Combine like terms:

$$ -18x^3 + 6x^2-45x^2-12x + 15x-30 = \\ -18x^3-39x^2+3x-30 $$

Polynomial Operations Calculator