Finding a solution of monomial

What is monomial

A monomial is an expression that could be a numeral, a variable, or the product of numerals and variables. A monomial is a product of positive integer powers of a fixed set of variables  together with a coefficient. A monomial can also be thought of as a nonzero summand of a polynomial. A monomial with the coefficient excluded is usually called a term. A polynomial with one term is called as monomial. The following are all monomials: 5x3, 8, and 4xy.

 

 

  • A monomial can be a constant number or a variable expression.     
  • A monomial should not have negative and fractional exponents.      
  •  Example: a- 2 and a1/2(are not monomials.)     
  • A monomial multiplied by a monomial is also a monomial.
  • A monomial multiplied by a constant is also a monomial.

Examples of Monomial

  • 5, xy, 36x2y, a, 14b are the examples of monomial.
  • 8x – 1, 2x2 + 3x + 6 are not monomials.

 

Which of the following expressions is a monomial?

A. 9xy

B. 7x + 3

C. y- 2

Solution:

Step 1: A monomial is an algebraic expression with only one term.

Step 2: 7x + 3 is not a monomial as there are two terms in the expression. [7x and 3 are the two terms.]

Step 3: y- 2 is not a monomial as it is having a negative exponent.

Step 4: But, 9xy is a monomial as it is having only one term in the expression. [9xy is the only one term.]

 

 

Problems:

1 . Divide 14x - 8 by 2.

 

Solution:

Step 1 : 14x - 82

Explanation: [Original expression.]

 
 

Step 2 : = 14x2 - 82

Explanation: [Divide each term by 2.]

 
 

Step 3 : = 2(7x)2 - 2(4)2

Explanation: [Find the common factors.]

 
 

Step 4 : = 7x - 4

Explanation: [Divide out common factors.]

 

2. Divide 14z - 8 by 2.

Solution:

Step 1 : 14z - 82

Explanation: [Original expression.]

 
 

Step 2 : = 14z2 - 82

Explanation: [Divide each term by 2.]

 
 

Step 3 : = 2(7z)2 - 2(4)2

Explanation: [Find the common factors.]

 
 

Step 4 : = 7z - 4

Explanation: [Divide out common factors.]