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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).

 Apr 13, 2020
 #1
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+1

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

 Apr 14, 2020
 #2
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+1

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

 Apr 14, 2020

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