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Polynomials

Polynomials, Terms and Degree

For any non-negative integer n, xn is called a power of x (read x-to-the-power-n).

We call n the exponent of the power. We define x0 =1.

We assume that you are familiar with the basic rules of exponents.

Exercise 1.

Before continuing, test your knowledge of the rules of exponents. See computer notation for how to enter your answers.

Write your solution in terms of a single power of x:

 A = 2x2 B = 3x3 AB = A = 2x3 B = - 3 A2B = A = 2 B = -2x5 A/B = A = 3x2 B = 4x2 A+B = A = 3x2 B = 5x -2 AB =

A polynomial in x is the result of adding constant multiples of powers of x. Here are some examples:

(a constant polynomial)

Each product in the sum is called a term of the polynomial.

The largest exponent of the terms is called the degree of the polynomial.

We define the degree of a constant polynomial to be zero.

In the above examples, the polynomials are of degrees 0, 1, 2, and 3 respectively.

A polynomial of degree 1 is also known as a linear polynomial. A polynomial of degree 2 is called a quadratic polynomial and a polynomial of degree 3 is called a cubic polynomial.

Exercise 2A.

Find the degree of the following polynomials:

 Find the degree of the following polynomial: x +  x +  x

 Degree of Polynomial

Exercise 2B.

Determine whether or not the following functions are polynomials:

 Polynomial x +  x +    x