Introduction to Polynomials – Naming Polynomials by Number of Terms – Practice Problems

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An algebraic expression is constructed from constants, variables, and the algebraic operations of addition, subtration, multiplication, division, and exponentiation. A polynomial is an algebraic expression where the exponents of variables must be whole numbers, including zero.

Some examples of polynomials are: 5, x, 5y²z, (a + b), (3x – 2y + 5y²z), (a³+ 2b – c + 1). There are four types of polynomials:
      1.) monomials: polynomials that have exactly one term (e.g. 5, x, 5y²z),
      2.) binomial: polynomials that have two terms (e.g. a + b),
      3.) trinomial: polynomials that have three terms (e.g. 3x – 2y + 5y²z), and
      4.) multinomial: polynomials that have four or more terms (e.g. a³ + 2b – c + 1).

When working with polynomials, it is important to keep in mind that:
1. All polynomials are algebraic expression but NOT all algebraic expressions are polynomials.
2. A polynomial that is only a variable has a coefficient and exponent that is 1; e.g. x, y, z
3. A polynomial that is a constant has a variable with zero exponent; e.g. 3x^0 or 3.

Polynomials, just like numbers, can be simplified by using a set of operations defined on polynomials, which are built from the algebraic operations and rules of arithmetic.

Polynomials are a powerful tool for figuring out the relationships between different patterns. Whether it is finding out how the weather patterns in the Bermuda triangle relate to the weather patterns in Los Angeles, or seeing if the antiaging effects of a drug on mice will tell us something about how the drug will affect humans, polynomials are always involved.

Perform arithmetic operations on polynomials.

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Exercises in this Practice Problem
Identify which of the following statements about monomials are true.
Find the term representing the cost of Bella's quinceanera.
Analyze the following terms.
Establish the polynomial representing the total cost of Bella's next shopping trip.
Decide if the given term is a monomial, binomial, trinomial, or polynomial.
Simplify the monomials and then add them together to make a polynomial.