polynomial

Meanings

• noun

  A polynomial is an expression consisting of variables and coefficients, involving operations of addition, subtraction, multiplication, and non-negative integer exponents.

  - "The quadratic polynomial x^2 + 3x + 2 equals 15 when x is 2."
  - "The roots of the polynomial ax^2 + bx + c can be found using the quadratic formula."

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Variants

List of all variants of polynomial that leads to same result
polynomial , polynomials , characteristic polynomial , characteristic polynomials

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Etymology

origin and the way in which meanings have changed throughout history.

The term 'polynomial' comes from the Greek words 'polys' meaning 'many' and 'nomos' meaning 'rule'. A polynomial is a mathematical expression that follows a set rule or pattern with multiple terms.

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Trivia

Any details, considerations, events or pieces of information regarding the word

1. The highest degree polynomial with integer coefficients and real roots is called the 'Waring tower' or 'Waring's chain'. It was proven by Leonard Eugene Dickson in 1913 that the degree of this polynomial is 13.

2. The study of polynomials is called 'algebra'. Algebra originated in ancient Babylonian mathematics around 2000 BCE.

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Related Concepts

informations on related concepts or terms closely associated with the word. Discuss semantic fields or domains that the word belongs to

1. Coefficient: A constant term in a polynomial expression.

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

3. Roots: The solutions of a polynomial equation.

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Culture

Any cultural, historical, or symbolic significance of the word. Explore how the word has been used in literature, art, music, or other forms of expression.

Polynomials have been used extensively in various fields of mathematics, physics, engineering, and computer science. They have applications in solving equations, modeling physical phenomena, and analyzing data.

How to Memorize "polynomial"

1. visualize
   

   - Visualize the polynomial as a collection of terms, each term being a variable raised to a power and multiplied by a constant coefficient.
   - Create a mental image of the polynomial as a graph, with the x-axis representing the variable and the y-axis representing the value of the polynomial.

2. associate
   

   - Associate the polynomial with a familiar equation, such as x^2 + 1 = 0, which has the solutions x = ±i.
   - Remember that the degree of a polynomial is the highest power of the variable.

3. mnemonics
   

   - Create a mnemonic phrase, such as 'Please Excuse My Dear Aunt Sally' (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) to remember the order of operations when simplifying polynomials.

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