Let f(x) be a polynomial such that f(0)=4, f(1)=5, and f(2)=10. Find the remainder when f(x) is divided by x(x-1)(x-2).
The answer is in the form ax^2+bx+c
C=4
A+B+C=5
4A+2B+C=10
A+B=1
4A+2B=6-->2A+B=3
A=2, B=-1, C=4
So the answer is 2x^2-x+4
+9519 Let f(x) = x(x - 1)(x - 2) Q(x) + R(x), where Q and R are polynomials which represents quotient and remainder respectively.
Let R(x) = ax^2 + bx + c.
f(0) = 4
R(0) = 4
c = 4
f(1) = 5
R(1) = 5
a + b + c = 5
a + b = 1 --- (1)
f(2) = 10
R(2) = 10
4a + 2b + c = 10
4a + 2b = 6 --- (2)
(2) - 2 * (1) : 2a = 4
a = 2
2 + b = 1
b = -1
Therefore
R(x) = 2x^2 - x + 4
