Cubic, quadratic, linear, constant

The idea

Polynomials of degree 3, 2, 1 and 0 are called cubic, quadratic, linear and constant polynomials; a constant is of degree 0 because it can be written with x⁰.

Four polynomials

Polynomials get names from their degree. Here are four of them: 5y³ + y² + 2y − 1, x² + 5x + 1, 3z + 7 and the plain number 8.

How many different names do you think four polynomials of degrees 3, 2, 1 and 0 will need?

• One name for all of them
• Two names
• Four names, one for each degree

Name them

Read the degree under each polynomial. Then give it its name.

Names by degree

Polynomials of degree 3, 2, 1 and 0 are called cubic, quadratic, linear and constant polynomials. A constant such as 8 has degree 0, because it can be written as 8x⁰.

• Degree | Name | Example
• 3 | cubic | 5y³ + y² + 2y − 1
• 2 | quadratic | x² + 5x + 1
• 1 | linear | 3z + 7
• 0 | constant | 8 = 8x⁰

Notes

Degree 3 cubic, degree 2 quadratic, degree 1 linear, degree 0 constant (8 = 8x⁰).

• Degree | Name | Example
• 3 | cubic | 5y³ + y² + 2y − 1
• 2 | quadratic | x² + 5x + 1
• 1 | linear | 3z + 7
• 0 | constant | 8 = 8x⁰

Check yourself

5x³ − 2 is a…

What is a polynomial of degree 1 called?

The constant polynomial 8 can be written as 8x⁰. What is its degree?

Answer: 0

The power of x in 8x⁰ is 0, so the degree is 0.

Which of these is a quadratic polynomial?

• quadratic polynomial. Quadratic means degree 2. The highest power here is 3.
• linear polynomial. Linear means degree 1.
• cubic polynomial — correct. Yes. The highest power is 3.
• quadratic. Quadratic is degree 2.
• constant. Constant is degree 0.
• cubic. Cubic is degree 3.
• linear — correct. Yes. 3z + 7 and 2x are linear polynomials.
• x² + 5x + 1 — correct. Yes. The highest power is 2.
• 3z + 7. That is linear: the highest power is 1.
• 5y³ + y² + 2y − 1. That is cubic: the highest power is 3.
• 8. That is a constant polynomial.