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.

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Introduction to Algebra

• Addition of Literals
• Subtraction of Literals
• Multiplication of Literals
• Division of Literals

• Constants and Variables

• Coefficient

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