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

$$ \begin{aligned} P(x) &= 6x^3+16x^2+16x+11 \\ Q(x) &= -2x^2+x \\ \end{aligned} $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|c|}\hline & \color{blue}{6x^3} & \color{blue}{16x^2} & \color{blue}{16x} & \color{blue}{11} \\ \hline \color{blue}{-2x^2} & & & & \\ \hline \color{blue}{x} & & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|c|}\hline & \color{blue}{6x^3} & \color{blue}{16x^2} & \color{blue}{16x} & \color{blue}{11} \\ \hline \color{blue}{-2x^2} & \color{orangered}{-12x^5} & \color{orangered}{-32x^4} & \color{orangered}{-32x^3} & \color{orangered}{-22x^2} \\ \hline \color{blue}{x} & \color{orangered}{6x^4} & \color{orangered}{16x^3} & \color{orangered}{16x^2} & \color{orangered}{11x} \\ \hline \end{darray} $$

Combine like terms:

$$ -12x^5-32x^4 + 6x^4-32x^3 + 16x^3-22x^2 + 16x^2 + 11x = \\ -12x^5-26x^4-16x^3-6x^2+11x $$

Polynomial Operations Calculator