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Maths / Polynomials / Factorization into Monomials

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Factorization into Monomials

Factors An algebraic expressions is a product of numbers or algebraic terms, then each of these numbers and terms are called the factors of the given algebraic expression and the algebraic expression is called the product of these terms.

Factorization When an algebraic expression is written as the product of two or more factors is called Factorization.

Factorization into Monomials:

Factorization into monomial means that expressing a algebraic expression as product of monomials.

Illustration: All possible factors of $3x^{2}y.$ are

Solution: The algebraic expression can be represented as.

$3x^{2}y=1times 3x^{2}y=3times x^{2}y=3xtimes xy=3xytimes x=x^{2}times 3y=ytimes 3x^{2}$

Thus, the possible factors of $3x^{2}y$ are

$1,3x^{2}y,3,x^{2}y,3x,xy,3xy,x,x^{2},3y,y,3x^{2}$

Greatest Common Factor ( GCF ) or Highest Common Factor ( HCF )

The greatest common factor of given monomials is the common factor having greatest coefficient and highest power of the variables. To find the GCF of two or more monomials the following step are to be performed .

Step I Write the given monomials.

Step II Find the greatest common numerical coefficient of each monomial.

Step III Find all the common literals appearing in the given monomials.

Step IV The product of greatest common numerical coefficient and all the common literals is the required GCF.

Illustration: Find the GCF of three monomials $3x, 21x^{2}$ and 15xy.

Solution: The GCF of three monomials $3x, 21x^{2}$ and 15xy can be clculated as

Greatest common numerical coefficient is 3

The common literal is x

So the GCF is 3x

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