Monomial is a Common Factor

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         


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)                   

(ii) 9xy2 + 12x2y - 18xy


9xy2 + 12x2y – 18xy

We can also write, 9xy2 = 3xy × 3y2, 12x2y = 3xy × 4x and 18xy = 3xy × 6

The H.C.F of the terms 9xy2, 12x2y, 18xy is 3xy.

Therefore, 9xy2 + 12x2y – 18xy = 3xy(3y + 4x – 6)

                                           = 3xy(4x + 3y – 6)

(iii) 12a2b - 9ab2 + 6ab


12a2b - 9ab2 + 6ab

HCF of 12a2b, 9ab2, 6ab is 3ab.

Therefore, 12a2b - 9ab2 + 6ab

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

(iv) 12m3 + 32m2n


12m3 + 32m2n

HCF of 12m3 and 32m2n is 4m2.

Therefore, 12m3 + 32m2n = 4m2(3m + 8n).

8th Grade Math Practice

From Monomial is a Common Factor to HOME PAGE

New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

Share this page: What’s this?