Question
Multiply polynomial $ \, \color{blue}{ 3x-2 } \, $ by $ \, \color{orangered}{ 4x^2-3x-5 }$.
Answer
$$ \left( \color{blue}{3x-2} \right) \cdot \left( \color{orangered}{4x^2-3x-5} \right) = 12x^3-17x^2-9x+10 $$
Explanation
We can multiply polynomials by using a GRID METHOD
Write one of the polynomials across the top and the other down the left side.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^2} & \color{blue}{-3x} & \color{blue}{-5} \\ \hline \color{blue}{3x} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^2} & \color{blue}{-3x} & \color{blue}{-5} \\ \hline \color{blue}{3x} & \color{orangered}{12x^3} & \color{orangered}{-9x^2} & \color{orangered}{-15x} \\ \hline \color{blue}{-2} & \color{orangered}{-8x^2} & \color{orangered}{6x} & \color{orangered}{10} \\ \hline \end{darray} $$Combine like terms:
$$ 12x^3-9x^2-8x^2-15x + 6x + 10 = \\ 12x^3-17x^2-9x+10 $$This page was created using
Polynomial Operations Calculator