Question

What will be the quotient and remainder if $(2m^3+m^2+m+9)÷(2m-1)$ ?

• A. Quotient = $(m^2+m+2)$
  Remainder = $\left(10\right)$
• B. Quotient = $(m^2+m+1)$
  Remainder = $\left(10\right)$
• C. Remainder= $(m^2+m+1)$
  Quotient= $\left(10\right)$
• D. Remainder= $(m^3+m+1)$
  Quotient= $(10m+2)$

Answer 1

The correct option is B Quotient = $(m^2+m+1)$

Remainder = $\left(10\right)$
Given: $(2m^3+m^2+m+9)÷(2m-1)$

$\begin{array}{c}{m}^2+m+1\\ (2m-1)2m^3+m^2+m+9\\ \underset{–}{2m^3-m^2-+}2\\ 2m^2+m+9\\ \underset{–}{2m^2-m-+}\\ 2m+9\\ \underset{–}{2m-1-+}\\ \underset{–}{10}\end{array}$
Quotient = $m^2+m+1$
Remainder = $10$