Factorization of algebraic expressions when a monomial is a common factor:

Factorization when a common monomial factor occurs in each term then;

(i) Write the algebraic expressions.

(ii) Find the H.C.F. of all the terms of the expression.

(iii) Divide each term of the expression by the H.C.F.

(iv) Keep the H.C.F. outside the bracket and the quotients obtained within the bracket.

Solved examples when a monomial is a common factor:

Factorize each of the following algebraic expressions.

(i) 10x + 15

**Solution: **

10x + 15

We can also write, 10x = 5 × 2x and 15 = 5 × 3

The H.C.F of 10x and 15 is 5

Therefore, 10x + 15 = 5(2x + 3)

9xy

We can also write, 9xy

The H.C.F of the terms 9xy

Therefore, 9xy

= 3xy(4x + 3y – 6)

(iii) 12a

12a

HCF of 12a

Therefore, 12a

= 3ab(4a - 3b + 2).

(iv) 12m

12m

HCF of 12m

Therefore, 12m

**8th Grade Math Practice**

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