Factors of Algebraic Expressions


Before we discuss about the factors of algebraic expressions let us recall the concept of factors and multiples. If we multiply 2, 3, 5 we get 30, i.e., 30 = 2 × 3 × 5. Here, 2, 3, 5 are the factors of 30.

So to find the factors of given numbers, we express it as the product of two or more numbers. Similarly, we can find the factors of algebraic expressions.

Factors of Algebraic Expressions:  If algebraic expressions is expressed as the product of numbers, algebraic variables or  algebraic expressions, then each of these numbers and  expressions is called the factor of algebraic expressions.


Factors of the Monomials: 

It consists of every variable, their product and the number that divides it exactly.

1. Write all the possible factors of 7mn2

Solution:



The possible factors of 7 are 1, 7.

The possible factors of mn2 are m, n, n2, mn, mn2.

Therefore, all the possible factors of 7mn2 are m, n, n2, mn, mn2, 1, 7, 7m, 7n, 7n2, 7mn and 7mn2.


2. Write down all the factors of 3x2y.

Solution:

The possible factors of 3 are 1, 3.

The possible factors of x2y are x, y, xy, x2, x2y.

Therefore, all possible factors of 3x2y are x, y, xy, x2, x2y, 1, 3, 3x, 3y, 3xy, 3x2, 3x2y.


Highest Common Factor (HCF) of Monomials: 

The H.C.F. of two or more monomials is the product of the H.C.F. of the numerical coefficients and the common variables with least powers.

1. Find the H.C.F. of 2m3n2, 10m2n3, 8mn4.

Solution:

The H.C.F. of 2, 10 and 8 is 2.

The common variables appearing are m and n.

The smallest power of m appearing in 3 monomials = 1

The smallest power of n appearing in 3 monomials = 2

Therefore, monomials of common variables with the smallest power = mn2

Therefore, H.C.F. of 2m3n2, 10m2n3, 8mn4 is 2mn2.





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