Question - Dividing a Cubic Polynomial by a Linear Monomial
Solution:
Given $$ P(x) = 2x^3 + 3x^2 - x - 5 $$ and $$ D(x) = x - 1 $$, we will perform polynomial long division.$$\begin{array}{r}2x^2+5x+4 \\x-1 \,|\overline{\, 2x^3 + 3x^2 - x - 5} \\-\underline{2x^3 - 2x^2} \\5x^2 - x \\-\underline{5x^2 - 5x} \\4x - 5 \\-\underline{4x - 4} \\-1\end{array}$$The quotient is $$ Q(x) = 2x^2 + 5x + 4 $$ and the remainder is $$ -1 $$.
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