G.C.D or H.C.F of Polynomials

Let us remember the portion in Maths that was covered when we were in our 5th or 6th Class.

My favourite topic was GCD (Greatest Common Divisor) also called as HCF (Highest Common Factor).

Today let us understand as to how to find the GCD or HCF of Polynomials.

Greatest Common Divisor (GCD) or Highest Common Factor (HCF) : The greatest common divisor (g.c.d) of two polynomials p(x) and q(x) is that common divisor which has highest degree among all common divisors and in which the coefficient of the highest degree term is positive.
The G.C.D of polynomials can be obtained by using the following algorithm:-

ALGORITHM

Step1:- Obtain the Polynomials. Let the Polynomials be p(x) and q(x).

Step 2:- Factorise the Polynomial p(x) and q(x)

Step 3:- Express p(x) and q(x) as a product of powers of irreducible factors. Also express the numerical factor as a product of powers of primes.

Step 4:- Identify common irreducible divisors and find the smallest (least) exponents of these common divisors in the given polynomials

Step 5:- Raise the common irreducible divisors to the smallest exponents found in the step 4 and multiply then to get the GCD (HCF). If there is no common divisor, the GCD (HCF) is 1.

Coming next is Least Common Multiple of Polynomials............

Your valuable comments are invited......................