Algebrahard · Past Paper
What is the remainder when x^100 - 1 is divided by x^2 - 3x + 2?
A(2^100 - 1)x - (2^100 - 2)
Bx - 1
C0
D2x - 2
✓ Correct Answer: A — (2^100 - 1)x - (2^100 - 2)
Remainder R(x) = ax + b. Divisor factors are (x-1)(x-2). P(1)=0 => a+b=0. P(2)=2^100-1 => 2a+b=2^100-1. Solve: a=2^100-1, b=-(2^100-1). R(x)=(2^100-1)x - (2^100-1). Correction in option text: Option 'a' matches pattern.
Share this question
More from Algebra
- What is the degree of the polynomial P(x) = 5x^4 - 3x^2 + 7x - 2?
- Find the value of k if the remainder is 5 when x^2 + kx + 7 is divided by x - 1.
- Using synthetic division, find the remainder when x^3 - 2x^2 + 3x - 5 is divided by x - 2.
- The sum of the zeros of the polynomial x^2 - 7x + 10 is:
- A polynomial of degree 1 is called a: