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

$$ \left( \color{blue}{x^2-x-2} \right) \cdot \left( \color{orangered}{2x+x-6} \right) = 3x^3-9x^2+12 $$

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

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

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

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

Combine like terms:

$$ 3x^3-3x^2-6x^2-6x + 6x + 12 = \\ 3x^3-9x^2+12 $$

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