How We Use Degrees of Polynomials:
To find the Degree of a polynomial, add the exponents for each term. The term with the highest sum will determine the degree.
When solving or graphing polynomial equations, the Degree of the Polynomial will indicate the number of possible solutions and the number of times the graph may cross the x-axis. A line (y = 5x + 2) will cross the x-axis once and have one solution because it has a Degree of 1. A quadratic equation, such as, may cross the x-axis zero, one or two times and have zero, one or two solutions.
Sample Math Problems
1. What degree is the following polynomial?
Solution:
The greatest degree is 7, so this is a Polynomial of Degree 7.
2. What degree is the following polynomial?
Solution: The greatest degree is 4, so this is a Polynomial of Degree 4.
3. What degree is the following polynomial?
Solution: This is a Polynomial of degree 11 because the first term has two exponents that add together to make 11, which is the greatest degree.
4. How many possible times could the following Polynomial cross the x-axis?
Solution: This polynomial may cross the x-axis up to 7 times because it is a Polynomial of Degree 7.
