The highest power
Degree of a polynomial
How big is it?
Look at x² + 5x + 1. It has a power 2, a coefficient 5 and three terms. One of these numbers tells how "big" the polynomial is.
Which number do you think describes the polynomial x² + 5x + 1?
What this lesson covers
The idea
The highest power of the variable in a polynomial is called its degree.
How big is it?
Look at x² + 5x + 1. It has a power 2, a coefficient 5 and three terms. One of these numbers tells how "big" the polynomial is.
Which number do you think describes the polynomial x² + 5x + 1?
- 5, the biggest number written
- 2, the highest power of x
- 3, the number of terms
Find the highest power
Look at the power on each variable. Tap the term with the highest power.
Degree
The highest power of the variable in a polynomial is called its degree.
The degree is not the biggest coefficient, not the first term and not the number of terms. Only the highest power counts.
- Polynomial | Degree
- x² + 5x + 1 | 2
- 5y³ + y² − 8 | 3
- 3z + 7 | 1
Notes
The degree of a polynomial is the highest power of its variable.
Check yourself
What is the degree of 7x⁴ + 3x² + 1?
Answer: 4
The powers are 4, 2 and none. The highest is 4.
What is the degree of 3z + 7?
What is the degree of 2x + 9x³ + 5?
Answer: 3
9x³ has the highest power, so the degree is 3.
A polynomial has the terms 100x, x² and 3. Its degree is…
- 1 — correct. Yes. 3z is 3z¹, so the highest power is 1.
- 2. There are 2 terms, but the degree is the highest power, which is 1.
- 3. 3 is the coefficient. The power of z is 1.
- 7. 7 is the constant. It is not a power.
- 1. 100x has power 1, but x² has a higher power.
- 2 — correct. Yes. The highest power is 2, from x².
- 100. 100 is a coefficient. It does not decide the degree.