2.4.1

Polynomials

Test yourself

Polynomials

You need to be able to name polynomials and give their degrees.

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Terminology

  • When a term in an expression is of the form axmax^m, where aa is a constant and mm is a whole number, it is called a monomial.
    • For example, 3x53x^5 is a monomial.
  • Similarly, a binomial is the sum or difference of two monomials.
    • 2x+6x42x + 6x^4 is a binomial.
  • A trinomial is the sum or difference of three monomials.
    • 1+4x5x21 + 4x - 5x^2 is a trinomial.
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Polynomials

  • The general term for the sums of monomials is polynomials.
    • 12x+4x217x5+3x121-2x + 4x^2 -17x^5 + 3x^{12} is a polynomial.
  • Polynomials can always be written in the form:
    • anxn+an1xn1+...+a2x2+a1x+a0a_n x^n + a_{n-1}x^{n-1}+ ... + a_2x^2 + a_1x + a_0
  • Where aia_i are real numbers that we call coefficients.
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Degree

  • The degree of a term is the exponent of its variable.
    • The degree of a constant is 0, as any constant a=ax0a = ax^0.
  • The degree of a polynomial is the highest degree of all its terms.
    • The degree of 3x35x+73x^3-5x+7 is 33.

Jump to other topics

1Proof

2Algebra & Functions

2.1Powers & Roots

2.2Quadratic Equations

2.3Inequalities

2.4Polynomials

2.5Graphs

2.6Functions

2.7Transformation of Graphs

2.8Partial Fractions (A2 Only)

3Coordinate Geometry

4Sequences & Series

5Trigonometry

6Exponentials & Logarithms

7Differentiation

8Integration

9Numerical Methods

10Vectors

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