GCD of a polynomial — lesson. Mathematics State Board, Class 9.

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Greatest common divisor:

The greatest common factor (

$GCD)$ of two or more polynomial is a polynomial of highest degree common to both the polynomials. In other words, the common factor of the polynomials with the highest degree. It is also called the Highest Common Factor

$(HCF)$ .

Example:

Consider the polynomials

$12xyz$ and

$3x$ .

Here the coefficients

$12$ and

$3$ have the only highest common divisor

$3$ .

Thus, the

$GCD$ of the numerical part is

$3$ .

Also, the variables

$xyz$ and

$x$ have

$x$ as the only common divisor with highest degree.

Hence, the

$GCD$ of the variable part is

$x$ .

Therefore, the

$GCD$ of the polynomials

$12xyz$ and

$3x$ is

$3x$ .

Procedure to find the $GCD$ by factorisation:

Resolve each polynomials or expressions into factors.
The product of common factors with highest degree will be the $GCD$ of the polynomial.
If the polynomials consists if numerical part, then the highest divisor common to both the coefficient part of the polynomials will be the $GCD$ of the numerical part.
Prefix the $GCD$ of the numerical part as a coefficient to the $GCD$ of the polynomial.

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4. GCD of a polynomial

Theory: