Polynomials

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Polynomials
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Polynomials

• A polynomial is a term or the sum or difference
  of two or more terms.
• A polynomial has no variables in the denominator.
• The degree of a term is the exponent of the
  variable (4x3 is a 3rd degree term).
• The degree of the polynomial is the same as the
  degree of the term with the highest degree.
• (x5 4x3 3x 2 is a fifth degree
  polynomial)
• Polynomials in standard form are in order of
  degree from highest to lowest with the constant
  at the end.

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Polynomials By Terms

• A polynomial with one term is called a monomial.
• A polynomial with two terms is called a binomial.
• A polynomial with three terms is called a
  trinomial.

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Polynomials by Degrees

• A first degree polynomial is linear.
• A second degree polynomial is quadratic.
• A third degree polynomial is cubic.
• A polynomial with no variable is called a
  constant.

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Examples 1 and 2

• Name the degree of each term and each polynomial.
  Put them in standard form.
• Degree of each term 5, 3, 1, and 0
• Degree of the polynomial 5
• Its in standard form.
• New Problem
• Degree of each term 1, 2, 0, and 3
• Degree of the polynomial 3rd
• In standard form, it is

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Example 3
An egg is thrown off the top of a building. Its
height in meters above the ground can be
approximated by the polynomial 300 2t 4.9t2,
where t is the time since it was thrown in
seconds.
How high is the egg above the ground after 5
seconds?
How high is the egg above the ground after 6
seconds?
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Example 4

• A firework is launched from a platform 6 feet
  about the ground at a speed of 200 feet per
  second. The firework has a 5-second fuse. The
  height of the firework in feet is given by the
  polynomial -16t2 200t 6, where t is the time
  in seconds. How high will the firework be when
  it explodes?