Question
Multiply polynomial $ \, \color{blue}{ 4x^3-3x-1 } \, $ by $ \, \color{orangered}{ x-1 }$.
Answer
$$ \left( \color{blue}{4x^3-3x-1} \right) \cdot \left( \color{orangered}{x-1} \right) = 4x^4-4x^3-3x^2+2x+1 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^3} & \color{blue}{-3x} & \color{blue}{-1} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{-1} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4x^3} & \color{blue}{-3x} & \color{blue}{-1} \\ \hline \color{blue}{x} & \color{orangered}{4x^4} & \color{orangered}{-3x^2} & \color{orangered}{-x} \\ \hline \color{blue}{-1} & \color{orangered}{-4x^3} & \color{orangered}{3x} & \color{orangered}{1} \\ \hline \end{darray} $$Combine like terms:
$$ 4x^4-3x^2-4x^3-x + 3x + 1 = \\ 4x^4-4x^3-3x^2+2x+1 $$This page was created using
Polynomial Operations Calculator