Monomial

Let Us Learn About Monomial

A monomial is an algebraic expression in which the only operations that appear between the variables are the product and the power of the natural exponent.

2x²y³z

Parts of a Monomial

Coefficient

The coefficient of a monomial is the number that multiplies the variable(s).

Literal Part

The literal part is constituted by the letters and its exponents.

Degree

The degree of a monomial is the sum of all exponents of the letters or variables.

The degree of 2x² y³ z is: 2 + 3 + 1 = 6

Similar Monomials

Two monomials are similar when they have the same literal part.

2x² y³ z is similar to 5x² y³ z

Degree of a monomial:

The sum of the degrees/exponents of each of the variables in a monomial is called the degree of monomial.

Note: In a non-variable monomial, that is a constant which is any number other than zero, degree is always zero. Like 6, 3, 4, 2 etc. Have a degree zero!

• Degree of a Monomial: The degree of a monomial is the sum of the exponents of all its variables. For example, the degree of xy is 2, the degree a^3 b of is 4, the degree of 12 is 0.
• Degree of a Polynomial: The degree of a polynomial is the greatest degree of any term in the polynomial. For example, the degree of x^5 - 5x^ 2 is 5, the degree of x^3+y^4-3x^2 = 2y is 4.

Solved Example on Degree

Find the degree of x^8y^6 + x^9 y^6.

Choices:

A. 8

B. 9

C. 16

D. 15

correct answer is d

Solution

Step 1: The degree of a polynomial is the greatest degree of any term in the polynomial.

Step 2: The degree of the second term in x^8y^6 + x^9 y^6 is ‘15’, which is the highest. So, the degree of the given polynomial is 15.

Related Terms for Degree

• Monomial
• Exponent
• Polynomial
• Variable
• Sum

• The degree of a monomial is the sum of the degrees in each of its variables.
• The degree of monomial is the sum of the exponents of the variable in the monomial.
• The degree of a nonzero constant term is 0.
  
• The constant 0 does not have a degree.

Example: Find the degree of monomial x⁷y³z².

Solution: Sum of the degree of in each variables is = 7+3+2 = 12.

Therefore the degree of the monomial is 12.

In our next we shall learn about degree of a polynomial