Question

What will be the quotient and remainder if $(x^3-4x^2+2x+5)÷(x-2)$?

• A. Quotient = $(x^2-2x+6)$
  Remainder = $\left(17\right)$
• B. Quotient = $(x^2-2x+9)$
  Remainder = $\left(17\right)$
• C. Quotient = $(x^3-2x^2+6)$
  Remainder = $\left(17\right)$
• D. Quotient = $(x^2-2x+6)$
  Remainder = $\left(17x^3\right)$

Answer 1

The correct option is A Quotient = $(x^2-2x+6)$

Remainder = $\left(17\right)$
Given: $(x^3-4x^2+2x+5)÷(x-2)$
$\begin{array}{c}{x}^2-2x+6\\ x-2x^3-4x^2+2x+5\\ \underset{–}{x^3-2x^2-+}2\\ -2x^2+2x+5\\ \underset{–}{-2x^2-4x++}\\ 6x+5\\ \underset{–}{6x-12-+}\\ \underset{–}{17}\end{array}$

Quotient = $(x^2-2x+6)$
Remainder = $\left(17\right)$