Definition of a polynomialBefore giving you the definition of a polynomial, it is important to provide the definition of a monomial Definition of a monomial: A monomial is a variable, a real number, or a multiplication of one or more variables and a real number with wholenumber exponents Examples of monomials and nonmonomials
Polynomial definition: A polynomial is a monomial or the sum or difference of monomials. Each monomial is called a term of the poynomial Important!:Terms are seperated by addition signs and subtraction signs, but never by multiplication signs A polynomial with one term is called a monomial A polynomial with two terms is called a binomial A polynomial with three terms is called a trinomial Examples of polynomials:
Difference between a monomial and a polynomial: A polynomial may have more than one variable. For example, x + y and x^{2} + 5y + 6 are still polynomials although they have two different variables x and y By the same token, a monomial can have more than one variable. For example, 2 × x × y × z is a monomial Exercices For all expressions below, look for all expressions that are polynomials. For those that are polynomials, state whether the polynomial is a monomial, a binomial, or a trinomial 1) 3.4 + 3.4x 2) z^{2} + 5z^{1} + 6 3) 8 4) 2c^{2} + 5b + 6 5) 14 + x 6) 5x  2^{1} 7) 4 b^{2}  2 b^{2} 8) f^{2} + 5f + 6 Answer: 1), 3), 4), 5), 6), and 8) are polynomials. 1), 5), and 6) are binomials. 3) is a monomial. 4) and 8) are trinomials 2) and 7) are not because they have negative exponents Notice that 6) is still a polynomial although it has a negative exponent. It is because it is the exponent of a real number, not a variable In fact, 5x  2^{1} = 5x + 1/2 = 5x + 0.5 It is subtle, but if you have any questions about the definition of a polynomial, feel free to contact me Related topics: Simplifying algebraic expressions Degree of a polynomial Adding polynomials Subtracting polynomials Multiplying polynomials 




