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) 8x
4 y – 7x 3 yz + 4/3 x 2 yz 2 - 2.5 xyz. What is the co-efficient of x 2 in the term 4/3x 2 yz 2 ?

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

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

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

Introduction to Algebra