Review question

# If we divide by $x-1$, the remainder is? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6790

## Solution

When $1 + 3x + 5x^2 + 7x^3 + \dots + 99x^{49}$ is divided by $x-1$ the remainder is

1. $2000$,

2. $2500$,

3. $3000$,

4. $3500$.

The remainder theorem tells us that when a polynomial $p(x)$ is divided by $x-1$ then the remainder is $p(1)$, which in this case is $1 + 3 + 5 + 7 + \dots + 99.$ This is an arithmetic progression, and so sums to $\frac{1}{2}\times 50(1+99) = 2500$ and the answer is (b).