Multiply polynomial $ \, \color{blue}{ -2g^3+11g^2-10g-14 } \, $ by $ \, \color{orangered}{ g-2 }$.

$$ \left( \color{blue}{-2g^3+11g^2-10g-14} \right) \cdot \left( \color{orangered}{g-2} \right) = -2g^4+15g^3-32g^2+6g+28 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|c|}\hline & \color{blue}{-2g^3} & \color{blue}{11g^2} & \color{blue}{-10g} & \color{blue}{-14} \\ \hline \color{blue}{g} & & & & \\ \hline \color{blue}{-2} & & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|c|}\hline & \color{blue}{-2g^3} & \color{blue}{11g^2} & \color{blue}{-10g} & \color{blue}{-14} \\ \hline \color{blue}{g} & \color{orangered}{-2g^4} & \color{orangered}{11g^3} & \color{orangered}{-10g^2} & \color{orangered}{-14g} \\ \hline \color{blue}{-2} & \color{orangered}{4g^3} & \color{orangered}{-22g^2} & \color{orangered}{20g} & \color{orangered}{28} \\ \hline \end{darray} $$

Combine like terms:

$$ -2g^4 + 11g^3 + 4g^3-10g^2-22g^2-14g + 20g + 28 = \\ -2g^4+15g^3-32g^2+6g+28 $$

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