Overview:
Monomial and polynomial expressions in algebra are ways to combine numbers and variables within an equation. Both types of expressions follow certain rules. They can be used in operations, similar to other numbers.
What Are Monomials?
Monomials are numbers or variables, or the product of numbers and variables. The exponents must be positive whole numbers. For example, an expression such as 9 is a monomial because it is a single number. A variable such as z4 is a monomial, because the exponent is a positive whole number. Similarly, – 3q9y2 is a monomial, because the negative number, -3, is not in the exponent.
What Are Not Monomials?
An expression such as 8y-4 is not a monomial. Although it has a whole number exponent, the exponent is negative. Similarly, 3y1/2 is not a monomial because the exponent is not a whole number. Also, an expression such as 4z2y + 1, is not a monomial, because it contains two separate monomials, 4z2y and 1. They are added together, rather than being the product of numbers and variables.
What Are Polynomials?
Polynomials are a larger set of algebraic expressions that include monomials. They can have more than one term, such as monomials added together. The expression 4z2y + 1 is the sum of monomials. It is called a binomial because it has two terms. Similarly, an expression such as 2a – 3n + 4 is a trinomial, because it has three terms that are added together as part of the same unit.
What Is the Degree of a Polynomial?
The degree of a polynomial is taken from the highest exponent used in its terms. For example, the expression 2x2 + y + 4 has the highest exponent of 2 in the term 2x2. It is also known as a quadratic polynomial. Linear polynomials, such as 2z + 3 are also common. An expression such as 5x3 + 1 is also known as a cubic polynomial.
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