# What is the remainder of (x^107+3x^98-4x^4-3)/(x-1)?

## What is the remainder of $\frac{{x}^{107} + 3 {x}^{98} - 4 {x}^{4} - 3}{x - 1}$?

Jan 25, 2018

Remainder is $- 3$

#### Explanation:

According to remainder theorem, when a polynomial $f \left(x\right)$ is divided by $x - \alpha$,

the remainder is f(alpha

Hence dividing ${x}^{107} + 3 {x}^{98} - 4 {x}^{4} - 3$ by $x - 1$,

we get a remainder

${1}^{107} + 3 \cdot {1}^{98} - 4 \cdot {1}^{4} - 3$

= $1 + 3 - 4 - 3$

= $- 3$