To find the Highest Common Factor i.e. H.C.F. of algebraic expressions, the

factorization method and process of continuous division are in practice in the

conventional system. We now apply' Lopana - Sthapana' Sutra, the 'Sankalana

vyavakalanakam' process and the 'Adyamadya' rule to find out the H.C.F in a

more easy and elegant way.

Question: Find the H.C.F. of x2 + 5x + 4 and x2 + 7x + 6.

__1. Factorization method:__

x2 + 5x + 4 = (x + 4) (x + 1)

x2 + 7x + 6 = (x + 6) (x + 1)

H.C.F. is ( x + 1 ).

__2. Continuous division process.__

x

^{2}+ 5x + 4) x^{2}+ 7x + 6 ( 1
x

^{2}+ 5x + 4
___________

2x + 2 ) x

^{2}+ 5x + 4 ( ½x
x

^{2}+ x
__________

4x + 4) 2x + 2 ( ½

2x + 2

______

0

Thus 4x + 4 i.e., ( x + 1 ) is H.C.F.

3. Lopana - Sthapana process i.e. elimination and retention or alternate

destruction of the highest and the lowest powers is as below:

i.e.,, (x + 1) is H.C.F

I think factorisation method is easier to find HCF of algebraic expression

ReplyDelete