polynomial

/,pɔli'noumjəl/

Thân thiện

A student graphs a polynomial on the coordinate plane.

Definition

1. Adjective:

   • Having the character of or relating to a polynomial: Describes an expression, equation, or function that is or can be expressed as a polynomial.

2. Noun:

   • A mathematical expression: A function that is the sum of a finite number of terms, where each term consists of a constant coefficient multiplied by a variable raised to a non-negative integer power.

Usage Examples

• Adjective:

  • The equation is a polynomial equation of degree three.
  • We need to simplify this polynomial expression.

• Noun:

  • The function f(x) = 3x² + 2x - 5 is a polynomial.
  • Solving this polynomial requires finding its roots.

Advanced Usage

• "Polynomial time": In computer science, refers to an algorithm whose running time is bounded by a polynomial expression in the size of the input.

  • Problems solvable in polynomial time are generally considered tractable.

• "Polynomial regression": A form of regression analysis where the relationship between variables is modeled as an nth degree polynomial.

  • We used polynomial regression to fit a curve to the data points.

Variants and Related Words

• Polynomial function (n): A function defined by a polynomial expression.

  • A quadratic function is a specific type of polynomial function.

• Monomial (n): A polynomial with only one term (e.g., 5x³).

• Binomial (n): A polynomial with exactly two terms (e.g., x + 1).
• Trinomial (n): A polynomial with exactly three terms (e.g., x² + 2x + 1).

Synonyms

• Multinomial (n): A less common synonym for a polynomial, especially one with multiple terms.
• Algebraic expression (n): A broader category that includes polynomials.

Related Phrases and Concepts

• Degree of a polynomial: The highest power of the variable in the polynomial.

  • The degree of the polynomial x⁴ + 2x is four.

• Coefficient of a polynomial: The constant number multiplying a variable term.

  • In the term 7x², the coefficient is 7.

• Root/Zero of a polynomial: A value for the variable that makes the polynomial equal to zero.

  • Finding the roots of the polynomial is a key task in algebra.

Học thuật

Adjective

1. having the character of a polynomial
   • a polynomial expression

Noun

1. a mathematical function that is the sum of a number of terms

Từ đồng nghĩa

• multinomial