Multiply polynomial $ \, \color{blue}{ n^2+4+2n } \, $ by $ \, \color{orangered}{ -3n+2 }$.

$$ \left( \color{blue}{n^2+4+2n} \right) \cdot \left( \color{orangered}{-3n+2} \right) = -3n^3-4n^2-8n+8 $$

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

$$ \begin{aligned} P(x) &= n^2+2n+4 \\ Q(x) &= -3n+2 \\ \end{aligned} $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{n^2} & \color{blue}{2n} & \color{blue}{4} \\ \hline \color{blue}{-3n} & & & \\ \hline \color{blue}{2} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{n^2} & \color{blue}{2n} & \color{blue}{4} \\ \hline \color{blue}{-3n} & \color{orangered}{-3n^3} & \color{orangered}{-6n^2} & \color{orangered}{-12n} \\ \hline \color{blue}{2} & \color{orangered}{2n^2} & \color{orangered}{4n} & \color{orangered}{8} \\ \hline \end{darray} $$

Combine like terms:

$$ -3n^3-6n^2 + 2n^2-12n + 4n + 8 = \\ -3n^3-4n^2-8n+8 $$

Polynomial Operations Calculator