Question

What will be the quotient and remainder if $(3x-3x^2-12+x^4+x^3)÷(2+x^2)$?

• A. Quotient = $(x^3+2x-5)$
  Remainder = $(x-1)$
• B. Quotient = $(x^2+4x-5)$
  Remainder = $(7x-2)$
• C. Quotient = $(x^2+x-5)$
  Remainder = $(x-2)$
• D. Remainder= $(x^2+x-5)$
  Quotient= $(x-2)$

Answer 1

The correct option is C Quotient = $(x^2+x-5)$

Remainder = $(x-2)$
Given $(3x-3x^2-12+x^4+x^3)÷(2+x^2)$
$\begin{array}{c}{x}^2+x-5\\ x^2+2x^4+x^3-3x^2+3x-12\\ \underset{–}{x^4+2x^2--}2\\ x^3-5x^2+3x-12\\ \underset{–}{x^3+2x--}2\\ -5x^2+x-12\\ \underset{–}{-5x^2-10++}\\ \underset{–}{x-2}\end{array}$
Quotient = $(x^2+x-5)$
Remainder = $(x-2)$