2.1 UNDERSTANDING POLYNOMIALS

• Term - a number or a product of a number and variables raised to powers
• Coefficient - numerical factor of a term
• Constant - – term which is only a number
• Monomial - A polynomial with one term
• Binomial - A polynomial with two terms
• Trinomial - A polynomial with three terms
• Degree - It is called "Exponent/s"
• Degree of Polynomial - Highest exponent (if the term has more than 1 variable, then add all exponents of that term)
• Coefficient - Number in front of variables
• Leading Term - term of highest degree.
• Leading Coefficient - The coefficient of the Leading term
• Constant term - the term without variable
• Missing term - the term that has 0 as its coefficient
• -3x⁴ - 4x² + x - 1

  Terms: -3x^4 -4x^2 x -1

  Degrees: 4 2 1 0

  Coefficients: -3 -4 1

  Degree of Polynomial: 4

  Leading Term: -3x^4

  Leading Coefficient: -3

  Constant Term: -1

  Missing Term: 0x
• -6x⁹ – 8x⁶y⁴ + x⁷y + 3xy⁵ - 4

  Terms: -6x^9 -8x^6y^4 x^7y 3xy^5 -4

  Degrees: 9 10 8 6 0

  Coefficients: -6 -8 1 3 0

  Degree of Polynomial: 10

  Leading Term: -8x^6y^4

  Leading Coefficient: -8

  Constant Term: -4

  Missing Term: 0x^7y
• Descending Order - exponents decrease from left to right.
• Ascending Order - exponents increase from left to right
• When working with polynomials, we often use Descending order.
• Arrange in Descending order using the power of x.

  -6x² – 8x⁶ + x⁸ + 3x - 4

  x^8 - 8x^6 - 6x^2 + 3x - 4
• Arrange in Descending order using the power of x.

  5x²y² + 4xy + 2x³y⁴ + 9x⁴

  9x^4 + 2x^3y^4 + 5x^2y^2 + 4xy
• Evaluating - Involves replacing the value of the variable(s) involved.
• Like terms - Terms that contains the exact same variables and exact same exponents.
• Only like terms can be combined using addition and subtraction.
• Polynomial Long Division - Is a method for dividing a polynomial by another polynomials of a lower degree.