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