Are algebraic expressions polynomials?

Algebra is a branch of mathematics that deals with equations consisting of coefficients and variables, where variables are unknown quantities. These equations are solved with certain formulas to gain a solution. These formulas are the combination of numbers and letters in which numbers represent known and letters represent unknown values. 

Algebraic expressions

The expressions are made up of variables, constants, and coefficients along with algebraic operations (addition, subtraction, division, multiplication, and exponential) are algebraic expression. There are three types of algebraic expressions.

• Monomial expression
• Binomial expression
• Polynomial expression

Polynomials

Polynomials are the expression made up of the combination of constants, variables only having non-negative powers, coefficient, and algebraic operations. 

Are algebraic expressions polynomial?

Algebraic expressions are considered polynomials when all the exponents present in the expression on the variable are whole numbers. For example, x³ + 3/4x + 9, etc. All polynomials are algebraic expressions but all algebraic expressions are not polynomials.

Polynomials are the combination of constants, variables, coefficients, algebraic operations, and whole number exponents on the variables. For example, 2x², 2x + 3 are some of the polynomials.

Whereas algebraic expressions are the combination of constants, variables, coefficients, algebraic operations, and all types of exponents being whole number, negative, or fractional. For example 2x + 3, x√x, etc.

Sample Question

Question 1: How to identify polynomials?

Answer:

An expression is said to be polynomial when all powers of the variable will be non-negative integers or whole numbers.

Question 2: Is 2 a polynomial?

Answer:

2 is not a polynomial because it is only one constant value and is called a monomial.

Question 3: What is a polynomial formula?
Answer:

The formula that expresses polynomial expressions or expressions having more than two terms is called the polynomial formula.

Question 4:  What is degree polynomial?

Answer:

The highest exponent on a polynomial is called a degree. And a polynomial with a degree is called a degree polynomial.

Question 5: What are the types of degree polynomial?

Answer:

• A polynomial with degree 1 is a linear polynomial
• A polynomial with degree 2 is a quadratic polynomial
• A polynomial with degree 3 is a cubic polynomial

Question 6: Is 7 an algebraic expression?

Answer:

7 is not an algebraic expression because an expression should have at least one variable and one algebraic operation.

Question 7: What is a numeric expression?

Answer:

The expressions That consist of numbers and operations but do not include variables is called numeric expression. For example 10 + 5, 50 – 2,etc.