The highest power names it
Which term (one part of the sum) of 3x² − 4x + 7 decides its degree? Change the first power and watch.
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x³ + 4x + 9. The powers are 3, 1 and 0. Step 1 of 3
x³ + 4x + 9. The powers are 3, 1 and 0.- The highest power is 3. Circle it.
- The degree is 3.
The rule
The term 3x² decides it, because 2 is the highest power.
The degree is the highest power of the letter. The order of the terms does not matter. If two terms share the top power, that power is the degree.
7x + 2has powers 1 and 0. Its degree is 1.3x + 7x²has powers 1 and 2. Its degree is 2.9 + 4x + x³has powers 0, 1 and 3. Its degree is 3.
The number in front of a letter is its coefficient. In 3x² − 4x + 7, the coefficient of x² is 3. A plain number, here 7, is the constant term.
| Degree | Name | Example |
|---|---|---|
| 0 | constant | 5 |
| 1 | linear | 7x + 2 |
| 2 | quadratic | 3x + 7x² |
| 3 | cubic | x³ + 4x + 9 |
A rule of degree 1 is called linear. This chapter is about linear rules.
Watch out!
7x + 2 has two terms, but its degree is not 2. Count powers, not terms. Its powers are 1 and 0, so its degree is 1.