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.
|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!
|1||Linear||x – 5|
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:
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.
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|
How to Writing it
Instead of saying “the degree of (whatever) is 3” we write it like this:
deg(2x3−x2+3) = 3