Polynomials and their degree

Expressions like 4x, x² + 1, 2y – 5 and 5y³ + y² + 2y – 1 use one variable and its powers. They are called one-variable (or univariate) polynomials, or just polynomials.

The degree is the highest power of the variable:

• 5y³ + y² + 2y – 1 has degree 3: a cubic polynomial;
• x² + 5x + 1 has degree 2: quadratic;
• 3z + 7 has degree 1: linear;
• the number 8 is 8x⁰, degree 0: a constant polynomial.

Keep the sign with the number. In 5y³ + y² + 2y – 1, the coefficient of y³ is 5, of y² is 1 (y² means 1 × y²), of y is 2, and the constant term is –1.

A missing power has coefficient 0. In 4z³ + 5z² – 11 there is no z term, so the coefficient of z is 0.

To find a polynomial's value, put the number in place of the variable: 5x² – 3x + 7 at x = 1 is 5 – 3 + 7 = 9.