Question

Solve by remainder theorem when $x^4+x^3-2x^2+x+1$ is divided by $x-1$

Answer 1

We have,

Dividend $x^4+x^3-2x^2+x+1.....\left(1\right)$

Divisor$x-1$

Put divisor is equal to zero.

$x-1=0$

$x=1$

Put this value in equation (1),

$f\left(x\right)=1^4+1^3-2(1{)}^2+1+1$

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

$=2-2+2$

$=2$

This is the right answer.