Question

What will be the quotient and remainder if $(a^4-a^3+a^2-a+1)÷(a^3-2)$?

• A. Quotient = $(a+51)$
  Remainder = $(a^4+a-1)$
• B. Quotient = $(a-1+a^4)$
  Remainder = $(a^2+a-11)$
• C. Quotient = $(a^2-1)$
  Remainder = $(2a^2+a-1)$
• D. Quotient = $(a-1)$
  Remainder = $(a^2+a-1)$

Answer 1

The correct option is D Quotient = $(a-1)$

Remainder = $(a^2+a-1)$
Given:$(a^4-a^3+a^2-a+1)÷(a^3-2)$
$\begin{array}{c}a-1\\ a^3-2a^4-a^3+a^2-a+1\\ \underset{–}{a^4-2a-+}2\\ -a^3+a^2+a+1\\ \underset{–}{-a^3+2+-}\\ \underset{–}{a^2+a-1}\end{array}$
Quotient = $(a-1)$
Remainder = $(a^2+a-1)$