Polynomials

Definitions

• A term is a product of factors.
  
  Examples:
  
  

  -3x³ ,   9x² y³ ,   7x,    y,    5
  
  

  A term may have one or more factors.
  
  
• The numerical coefficient of a term is the numerical factor.
  
  Examples:
  
  

  Term     Numerical Coefficient
  
  -5³          -5
  
  4xy           4
  
   x            1    Since x = 1(x) the understood numerical factor is 1..
  
  -y           -1    Since -y = -1(y) the understood numerical factor is -1
  
  

• A polynomial in a single variable is a sum or difference of terms where each term is either a constant or a constant times a variable to a positive integer power.
  
  Examples:
  
  

  7x²  - 3,      2x³  + 3x - 6,      5x,      9
  
  

• The degree of a term in a single variables exponent on the variable if term involves a variable. The degree of a constant is zero.
  
  Examples:
  
  

  Term    Degree
  
  15x³     3
  
  -7x²     2
  
  4x       1
   
  5        0

• The degree of a polynomial in a single variable is defined to be the same as the degree of its term of highest degree, hence the highest power of that variable appearing in the polynomial. If no variable appears, that is, if polynomial is a constant, the degree of the polynomial is zero.
  
  Examples:
  
  

  Polynomial          Degree
  
  7x²  - 3             2
  
  2x³  + 3x - 6        3
  
  5x + 4               1
  
  9                    0
  

• Monomial: A polynomial of one term.
  
  Example: 7t²
  
  
• Binomial: A polynomial of two terms.
  
  Example: 2x - 3
  
  
• Trinomial: A polynomial of three terms.
  
  Example: 5x² - 7x + 10
  
  

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