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

$$ \left( \color{blue}{4x-3} \right) \cdot \left( \color{orangered}{3x^2-5x-8} \right) = 12x^3-29x^2-17x+24 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-5x} & \color{blue}{-8} \\ \hline \color{blue}{4x} & \color{orangered}{12x^3} & \color{orangered}{-20x^2} & \color{orangered}{-32x} \\ \hline \color{blue}{-3} & \color{orangered}{-9x^2} & \color{orangered}{15x} & \color{orangered}{24} \\ \hline \end{darray} $$

Combine like terms:

$$ 12x^3-20x^2-9x^2-32x + 15x + 24 = \\ 12x^3-29x^2-17x+24 $$

Polynomial Operations Calculator