EUCLID'S DIVISION ALGORITHM FOR POLYNOMIALS

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If p ( x ) and g ( x ) are two polynomials such that g ( x ) ≠  0, then you can find polynomials r ( x ) and q ( x )  that are related as following:

EUCLID'S DIVISION ALGORITHM FOR POLYNOMIALSp ( x ) = g ( x ) ✕ q ( x ) + r ( x )

Where r ( x ) = 0 or degree of r ( x ) < degree of g ( x )

This result is known as Euclid’s Division Algorithm for polynomials.

Example: Let p ( x ) = x3 – 3x2 + 5x – 3 and g ( x ) = x2 – 2
Now divide p ( x ) by g ( x )

You will get quotient as q ( x ) = x – 3 and remainder as r ( x ) = 7x - 9

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