Module - Polynomials
Introduction - Animal Populations

Anyone who hunts knows that they can only do this during the designated season. This is to make sure that the animal population is not depleted. However, if left uncontrolled, an animal population develops polynomially. This means that if one animal has and average of 3 offspring, then each of the 3 babies will have an average of 3 offspring (a total of 9), and those 9 babies will average 3 offspring each (a total of 27), and so on.

The number of descendants of one animal, written as a polynomial, can be expressed as x + x^2 + x^3 + x^4 where x is the number of offspring an animal has. So, if an animal has an average of 8 offspring in its lifetime, it will probably have 4680 (8 + 8^2 + 8^3 + 8^4) descendants in four generations. Luckily, animal populations are controlled naturally by predators, disease, starvation, and natural competition.

• Use the following terms in a written paragraph to describe the key concepts of this unit.
  • polynomial
  • monomial
  • binomial
  • trinomial
  • simplify
  • decimal notation
  • scientific notation
  • degree
  • constants
  • FOIL method
• Multiply monomials and simplify expressions with powers of monomials.
• Divide monomials and simplify expressions with quotients of monomials and negative exponents.
• Express numbers in scientific and decimal notation.
• Find products and quotients of numbers expressed in scientific notation.
• Find the degree of a polynomial.
• Arrange the terms of a polynomial in ascending and descending order.
• Add and subtract polynomials.
• Multiply a monomial and a polynomial and simplify expressions with polynomials.
• Use FOIL to multiply binomials.
• Multiply polynomials by using the distributive property.
• Multiply special binomials by using a pattern.