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

$$ \begin{aligned} P(x) &= 10x^3-5x^2-3 \\ Q(x) &= 2x+5 \\ \end{aligned} $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{10x^3} & \color{blue}{-5x^2} & \color{blue}{-3} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{5} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{10x^3} & \color{blue}{-5x^2} & \color{blue}{-3} \\ \hline \color{blue}{2x} & \color{orangered}{20x^4} & \color{orangered}{-10x^3} & \color{orangered}{-6x} \\ \hline \color{blue}{5} & \color{orangered}{50x^3} & \color{orangered}{-25x^2} & \color{orangered}{-15} \\ \hline \end{darray} $$

Combine like terms:

$$ 20x^4-10x^3 + 50x^3-6x-25x^2-15 = \\ 20x^4+40x^3-25x^2-6x-15 $$

Polynomial Operations Calculator