What is the Degree?
Find the highest power in a polynomial. Watch how terms combine.
Equation
y = (x^2 + 4*x) / x^2
Graph
Table
| x | y |
|---|---|
| 1 | 5 |
| 2 | 3 |
| 3 | 2.33 |
| 4 | 2 |
| 5 | 1.8 |
| 6 | 1.67 |
| 7 | 1.57 |
| 8 | 1.5 |
| 9 | 1.44 |
| 10 | 1.4 |
What this lesson covers
What you do
You shape the function y = (x^2 + n*x) / x^2 and watch the graph answer.
Challenges to clear
- Set n = 2 and check x = 5: the ratio is 1.4 — the x² term is taking over.
- At x = 10 it is 1.2, closing in on 1: the DEGREE-2 term dominates the polynomial.
- A third term joins the race. Set the x coefficient n to 3.
- Now slide the constant c until x = 2 reads 3.75. Then look far right: the ratio still creeps toward 1 — the degree-2 term beats everything below it.
Check yourself
Why does the term with the highest power (x^2) determine the degree, even if its coefficient is small?
What is the degree of the polynomial 5x^3 + 100x^2 + 1000x?
- Because it grows the fastest as x increases — correct
- Because it is written first in the equation
- Because coefficients don't matter
- Because x^2 is always larger than x
- 2, because 100 is the largest coefficient
- 3, because x^3 has the highest power — correct
- 1000, because it is the largest number
- 6, because 3+2+1=6
Think about it
- As x grows, which term wins: x² or n·x?