# Coefficient

Coefficient is any of the factors with the sign of the term.

Examples :

(i) Find the co-efficient, monomial 3xy

co-efficient of y ---> 3x,

co-efficient of x ----> 3y

and the co-efficient of xy -----> 3.

(ii) Find the co-efficient of x ,y and xy,in the binomial -6xy + 8.

The co-efficient of x in the term -8xy ---> -8y,

the co-efficient of y ----> -8x

and the co-efficient of xy ----> -8.

Write down the co-efficients of the expression :

1) 8x4y – 7x3yz + 4/3 x2yz2 - 2.5 xyz. What is the co-efficient of x2 in the term 4/3x2yz2?

Solution :
The co-efficient of x 2 in the term 4/3 x2yz2 is 4/3 yz2

2) Write down the co-efficients of a, ab, and abc in the term 4a2b2c of the algebraic expression 4a 4b2c – 3a3b2c + 3/2 ab3c2.

Solution :
The given algebraic expression has three terms, namely, 4a 4b2c – 3a3b2c and 3/2 ab3c2
Consider the term , 4a4b2 c
We have, 4a4b2 c = 4a . a3b2c.
∴ Co-efficient of a, in 4a4b2 c is 4 a3b2c.
Also, 4a4b2 c = 4a3 . ab . bc
∴ Co-efficient of ab in 4a4b2 c is 4a3b2c.
Again, 4a4b2 c = 4 . abc . a3b.
∴ Co-efficient of abc in 4a4b2 c is 4a3b.

Introduction to Algebra