Multiply polynomial $ \, \color{blue}{ 9x^4-30x^3+46x^2-32x+8 } \, $ by $ \, \color{orangered}{ 2x+5 }$.

$$ \left( \color{blue}{9x^4-30x^3+46x^2-32x+8} \right) \cdot \left( \color{orangered}{2x+5} \right) = 18x^5-15x^4-58x^3+166x^2-144x+40 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|c|c|}\hline & \color{blue}{9x^4} & \color{blue}{-30x^3} & \color{blue}{46x^2} & \color{blue}{-32x} & \color{blue}{8} \\ \hline \color{blue}{2x} & & & & & \\ \hline \color{blue}{5} & & & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|c|c|}\hline & \color{blue}{9x^4} & \color{blue}{-30x^3} & \color{blue}{46x^2} & \color{blue}{-32x} & \color{blue}{8} \\ \hline \color{blue}{2x} & \color{orangered}{18x^5} & \color{orangered}{-60x^4} & \color{orangered}{92x^3} & \color{orangered}{-64x^2} & \color{orangered}{16x} \\ \hline \color{blue}{5} & \color{orangered}{45x^4} & \color{orangered}{-150x^3} & \color{orangered}{230x^2} & \color{orangered}{-160x} & \color{orangered}{40} \\ \hline \end{darray} $$

Combine like terms:

$$ 18x^5-60x^4 + 45x^4 + 92x^3-150x^3-64x^2 + 230x^2 + 16x-160x + 40 = \\ 18x^5-15x^4-58x^3+166x^2-144x+40 $$

Polynomial Operations Calculator