Question

Divide the polynomial $3x^4-4x^3-3x-1$ by x-1 and then find the remainder.

• A. -4
• B. -5
• C. -6
• D. -7

Answer 1

The correct option is B

-5

Substitute x - 1 = 0 in the given polynomial

Remainder = 3$\times$1-4$\times$1-3$\times$1-1= -5

Alternative

By division algorithm

$$\begin{array}{c}3x^3-x^2-x-4\\ x-13x^4-4x^3-3x-1\\ \underset{–}{3x^4-3x^3}2\\ -x^3-3x-1\\ \underset{–}{-x^3+x^2}\\ -x^2-3x-1\\ \underset{–}{-x^2+x}\\ -4x-1\\ \underset{–}{-4x+4}\\ -5\end{array}$$