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```
find remainder x power 100is divided by xpower2-3x+2
find remainder x power 100is divided by xpower2-3x+2

```
8 years ago Latika Leekha
165 Points
```							Let us assume a(x) = x100 and b(x) = x2-3x+2We need to find the remainder P(x) when a(x) is divided by b(x).a(x) = b(x)Q(x) + P(x), where 0 ≤ deg P(x) < deg b(x)Nowx100 = (x2-3x+2) Q(x) + P(x) = (x-1)(x-2) Q(x) + (ax+b) (Since 0< deg P(x) <2, so P(x) is of the form ax + b)x100 = (x-1)(x-2) Q(x) + (ax+b)Now put x = 1, we geta + b = 1Putting x = 2, we get2a + b = 2100On solving these two equations, we obtain the values of a and b asa = 2100 - 1b = 2- 2100Hence, the required reminader isP(x) = ax+b = (2100 – 1)x + (2- 2100)Thansk & RegardsLatika LeekhaaskIITians Faculty
```
6 years ago
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