Question

What is the remainder when x^37 is divided by
x² - 4x + 3?



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Answer 1

Answer:

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Answer 2

Concept

We will divide the given equation by x^37 and then find out the remainder. To divide we will multiply by some suitable step by step value such that it can eliminate the x^2 and then -4x.

Given

Diviser=x^37

Dividend=x^2-4x+3

Find

We have to calculate the remainder after we divide x^2-4x+3 by x^37.

Solution

We see that if we multiply by x^-33 in x^37 we will get x^2 and when we multiply by -4x^-36 we will get -4x, therefore,

We can write this

x^2-4x+3=x^37*(x^-33-x^-36)+3

Since the term 3 can't be eliminated therefore it comes as the additional term.

Comparing this with

Dividend = divisor * quotient + remainder.

Hence the remainder is 3.

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