Multiply polynomial $ \, \color{blue}{ x+2 } \, $ by $ \, \color{orangered}{ x^2-5x+6 }$.

$$ \left( \color{blue}{x+2} \right) \cdot \left( \color{orangered}{x^2-5x+6} \right) = x^3-3x^2-4x+12 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-5x} & \color{blue}{6} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{2} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-5x} & \color{blue}{6} \\ \hline \color{blue}{x} & \color{orangered}{x^3} & \color{orangered}{-5x^2} & \color{orangered}{6x} \\ \hline \color{blue}{2} & \color{orangered}{2x^2} & \color{orangered}{-10x} & \color{orangered}{12} \\ \hline \end{darray} $$

Combine like terms:

$$ x^3-5x^2 + 2x^2 + 6x-10x + 12 = \\ x^3-3x^2-4x+12 $$

Polynomial Operations Calculator