Question

How are polynomials like and unlike monomials? Provide an example of a monomial and an example of a polynomial. How does the following example, (5+ (-7x2) + x), fit the definition of a polynomial?
What might a binomial and a trinomial be? Give an example of a polynomial of degree 3. Of degree 6.

Answer 1

A polynomial is the sum of at least one term. For example, x^3+1 is a polynomial. A monomial is a polynomial with only one term, such as 2x^2. A binomial is a polynomial with two terms, and a trinomial is one with three terms. The example you gave is a trinomial (which is also a polynomial). Degree of a polynomial is the largest sum of variable powers in any term of the polynomial. So, for example, x^2 y has degree 3, and x^3+x^2 also has degree 3. A sixth degree polynomial would be x^6-2x+1, for example.