Degree can mean several things in mathematics:
- In Geometry a degree (°) is a way of measuring angles,
- In Algebra “Degree” is sometimes called “Order”
Table of Contents
Degree of a Polynomial
A polynomial looks like this:
2x3 + 3x2 + x -1
The Degree (for a polynomial with one variable, like x) is the largest exponent of that variable.
More Examples:
| 2x | The Degree is 1 (a variable without anexponent actually has an exponent of 1) |
| 2x3 + 3x2 + x -1 | The Degree is 3 (largest exponent of x) |
| 3y2 + y5 − 1 | The Degree is 5 (largest exponent of y) |
| 3 – z5 + 4z7 | The Degree is 7 (largest exponent of z) |
Names of Degrees
When we know the degree we can also give it a name!
| Degree | Name | Example |
| 0 | Constant | 4 |
| 1 | Linear | x – 5 |
| 2 | Quadratic | x2−2x+4 |
| 3 | Cubic | 2x3−x2+3 |
| 4 | Quartic | 3x4−2x3+x−4 |
| 5 | Quintic | x5−4x3+3x2+2x |
Higher order equations are usually harder to solve:
- Linear equations are easy to solve
- Quadratic equations are a little harder to solve
- Cubic equations are harder again, but there are formulas to help
- Quartic equations can also be solved, but the formulas are very complicated
- Quintic equations have no formulas, and can sometimes be unsolvable!
Degree of a Polynomial with More Than One Variable
When a polynomial has more than one variable, we need to look at each term. Terms are separated by + or – signs:
xy2−2x+4
For each term:
- Find the degree by adding the exponents of each variable in it,
- The largest such degree is the degree of the polynomial.
xy2−2x+4
Checking each term:
- xy2 has a degree of 3 (x has an exponent of 1, y has 2, and 1+2=3)
- 2x has a degree of 1 (x has an exponent of 1)
- 4 has a degree of 0 (no variable)
The largest degree of those is 3 , so the polynomial has a degree of 3
Degree of a Polynomial in Fraction
We can work out the degree of a rational expression (one that is in the form of a fraction) by taking the degree of the numerator and subtracting the degree of the denominator.
Here are 3 examples
| Fraction | Degree of Numerator | Degree of Denominator | Subtracting the degree | Degree of Fraction |
 | 3 | 2 | 3-2 | 1 |
 | 2 | 2 | 2-2 | 0 |
 | 3 | 4 | 3-4 | -1 |
How to Writing it
Instead of saying “the degree of (whatever) is 3” we write it like this:
deg(2x3−x2+3) = 3
Degree Values
| Expression | Degree |
| 1/x | −1 |
| log(x) | 0 |
| √x | ½ |
| ex | ∞ |