Use polynomial long division to find the quotient and the remainder when $\displaystyle {4}{x}^{{3}}-{2}{x}^{{2}}+{4}{x}-{2}$ is divided by $\displaystyle {x}-{1}$. Also, check your answer by showing that $\displaystyle {4}{x}^{{3}}-{2}{x}^{{2}}+{4}{x}-{2}$ is equal to $\displaystyle {x}-{1}$ times the quotient, plus the remainder.

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dividend = quotient x divisor + remainder = $\displaystyle \times$ $\displaystyle +$