# Division Algorithm for Polynomials

## Definition

In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalised version of the familiar arithmetic technique called long division. It can be done easily by hand, because it separates an otherwise complex division problem into smaller ones.

## Notes

If p(x) and g(x) are any two polynomials with g(x) is not equal to 0, then we can find polynomials q(x) and r(x) such that p(x)= g(x) × q(x)+r(x). Here, p(x) is dividend, g(x) is divisor, q(x) is quotient and r(x) is the remiander.
Steps to divide polynomials with help of example p(x)= 4x+x^3+x^4-3x^2+5, g(x)= x^2+1-x
1) Arrange terms of dividend and divisor in decreasing order of their degrees. Therefore, p(x)= x^4+x^3-3x^2+4x+5, g(x)= x^2-x+1
2) Then use the Euclid formula to divide. Here by solving this we get that dividend is x^4+x^3-3x^2+4x+5, divisor is x^2-x+1, quotient is x^2+x-3 and remainder is 8

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Polynomials part 11 (Division Algorithm) [00:10:52]
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