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## 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
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