Degree (mathematics) facts for kids

The degree of a polynomial is a simple way to describe its "size" or "highest power." It tells you the biggest exponent you can find on any variable in the polynomial. Think of it like the most important number that defines how complex the polynomial is. We often write the degree using the symbol , where stands for the polynomial.

What is a Polynomial?

A polynomial is a special type of math expression. It's made up of terms added or subtracted together. Each term usually has numbers and variables (like x or y) multiplied together. The variables can only have whole number exponents (like 0, 1, 2, 3, etc.). You won't see variables under a square root or in the denominator of a fraction in a polynomial.

Finding the Degree

To find the degree of a polynomial, you just need to look for the term with the largest exponent on its variable.

Example 1: Simple Polynomial

Let's look at this polynomial: .

• The first term is Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): 2x^3 . The exponent on 'x' is 3.
• The second term is Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): -7x^2 . The exponent on 'x' is 2.
• The third term is . When you don't see an exponent, it's actually 1 (like Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): 5x^1 ).
• The last term is Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): -4 . This is a constant term. You can think of it as Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): -4x^0 , so its exponent is 0.

Comparing all the exponents (3, 2, 1, 0), the highest one is 3. So, the degree of the polynomial is 3.

Example 2: Different Variable

The name of the variable doesn't change how we find the degree. Consider the polynomial .

• The highest exponent on the variable 'y' is 5.
• This happens in the term Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): -6y^5 .

Therefore, the degree of this polynomial is 5.

Why is the Degree Important?

The degree of a polynomial is very important in algebra. It helps us understand how the polynomial behaves. For example, it can tell us how many solutions a polynomial equation might have.

Roots and the Fundamental Theorem

The Fundamental theorem of algebra is a big idea in math. It tells us that a polynomial of degree n will have n complex roots. A "root" is a value for the variable that makes the polynomial equal to zero. For example, a polynomial with a degree of 3 will have 3 roots. These roots can be real numbers or complex numbers.