Understanding Polynomials

What is a Polynomial?

A polynomial is an expression consisting of constants and variables. The only operations used in a polynomial function are addition, subtraction, multiplication, and exponentiation.

Polynomial Example

Types of Polynomials

The type of polynomial is determined by the number of terms in an expression.

Polynomial Example
Number of Terms Polynomial Name Example
1 Monomial 5x²
2 Binomial 3x + 2
3 Trinomial x² + 4x + 3
4 Quadrinomial x³ + 2x² + 5x + 7
5+ Polynomial x⁴ + 3x³ + 2x² + x + 6

Degree of a Polynomial

The degree of a polynomial is determined by the highest exponent on a variable.

Degree of Polynomial Degree Name Example
0 Constant 5
1 Linear 3x + 2
2 Quadratic x² + 4x + 3
3 Cubic x³ + 2x² + 5
4 Quartic x⁴ + x³ + x² + x + 1

Naming a Polynomial

Naming a polynomial is simple: it's a combination of the degree name with the polynomial type.

Examples:

  • Quadratic Binomial: x² + 3x + 1
  • Cubic Trinomial: x³ + 4x² + x
  • Quartic Polynomial: x⁴ + 2x³ + 5x² + 7x + 3
  • Cubic Quadrinomial: x³ + x² + x + 1

Test Your Knowledge

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