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Remainder Theorem

Posted by Ravi Kumar at Wednesday, January 5, 2011
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Most of you have a question of “what is remainder theorem?”
Here it is………….

When a polynomial function f(x) is divided by (x-a), the remainder is f(a)
For example, when x^2 – 2x + 5 is divided by x-1, the remainder will be f(1),
i.e. 12 – 2(1) + 5 = 4

We can see that if f(x) is divided by (x+a), then the remainder will be f(-a).
For example, when x^3 + x^2 -5x – 4 is divided by (x+1), then the remainder will be f(-1).
i.e., (-1)^3 + (-1)^2 – 5(-1) – 4. i.e. 1

If f(a) is zero it means that the remainder is zero. Hence we can say that (x-a) is a factor of f(x).

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