Concept 2.1
Degree: the Highest Power
Source: NCERT Mathematics, Class 106 minute lesson
Formal statement
The highest power of x in a polynomial p(x) is called its degree. A polynomial of degree 1 is linear, of degree 2 quadratic, and of degree 3 cubic.
The intuition
The degree is the polynomial's rank. 4x³ − x + 7 has three terms, but only one of them decides how it behaves for large x: the x³.
Count powers, not terms. x² + 1 and 5x² − 3x + 2 are both quadratic; 2x + x³ is cubic even though the x³ is written last.
The attention
Look at the highest power of x, wherever it is written.
4x³ − x + 7
Look hereNot here
- Look here
- The highest power of x. x³ is the highest power, so the degree is 3. It doesn't matter how big its coefficient is or where it sits.
- Not here
- The coefficient in front. The 4 is a coefficient. It stretches the term but never changes its degree.
- What it teaches
- Find the part that dominates. The rest is detail.