Question

Find the reminder when $x^4+x^3-2x^2+x+1$is divided by $x-1$

• A. 2
• B. 0
• C. 1
• D. 3

Answer 1

Answer:

A. 2

when a polynomial p(x) is divided by (x - a) for some number a , the reminder r = p(a)

When p(a) = 0 then (x -a) is a factor of p(x)

$p(x)=x^4+x^3-2x^2+x+1$

$x-1=0$

$\implies{x=1}$

$p(1)=1^4+1^3-2\times1^2+1+1$

$=1+1-2+1+1$

$=2$

Reminder r = 2