IDENTIFY THE TERMS AND COEFFICIENTS IN AN ALGEBRAIC EXPRESSION

A single variable or a constant or a combination of these as a product or quotient forms a term.

Terms can be added or subtracted to form an expression. In the expression 5x + 3 the term 5x is made of 2 factors and 5 and x while 3 is a single factor.

A numerical or constant quantity placed before and multiplying the variable in an algebraic expression

Identify the number of terms and coefficient of each term in the following expressions.

Example 1 :

2x⁵ + 3x³ - 12x² + 11x - 5

Solution :

Terms :

There are five terms in the above algebraic expressions.

Term 1 = 2x⁵

Term 2 = 3x³

Term 3 = -12x²

Term 4 = 11 x

Term 5 = -5

Coefficients :

Coefficient of x⁵ = 2

Coefficient of x³ = 3

Coefficient of x² = -2

Coefficient of x = 11

Constant term = -5

Example 2 :

3x³ + x² - 2

Solution :

Terms :

There are three terms in the above algebraic expression.

Term 1 = 3x³

Term 2 = x² 

Term 3 = -2

Coefficients :

Coefficient of x³ = 3

Coefficient of x² = 1

Constant term = -2 

Example 3 :

5x + 10

Solution :

Terms :

There are two terms in the above algebraic expression.

Term 1 = 5x

Term 2 = 10

Coefficients :

Coefficient of x = 5

Constant term = 10 

Example 4 :

3xy - 7x

Solution :

Terms :

There are two terms in the above algebraic expression.

Term 1 = 3xy

Term 2 = -7x

Coefficients :

Coefficient of xy = 3

Coefficient of x = -7

Example 5 :

x/3 - 7y + 8

Solution :

Terms :

There are three terms in the above algebraic expression.

Term 1 = x/3

Term 2 = -7y

Term 3 = 8

Coefficients :

Coefficient of x = 1/3

Coefficient of y = -7

Constant = 8

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