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GCD of Polynomial: Example
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GCD of Polynomial: Example

Example: Find the g.c.d. of the polynomials x2+ 7x + 12 and x2 + 3x.
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Solution: Let p(x) = x2+ 7x + 12
x2+ (4x + 3x) + 12
= (x + 3) (x + 4)
   q(x) = x2 + 3x
x . (x + 3)
Clearly, (x + 3) is the only common irreducible divisor with least exponent as 1. Therefore,
GCD = (x + 3)1 = (x + 3).
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