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The degree of a polynomial in one variable is
the greatest exponent of its variable.
The leading coefficient is the coefficient of the
term with the greatest degree.

Is the expression a polynomial in one variable? If it
is, state the degree and leading coefficient.

                       Yes; degree: 4 leading coefficient: 1

                        No; It contains two variables, a and b.

                        No; The term 2c–1 is not a monomial
                                 (dividing by the variable c).
Find   2

           2          2       2   2
               = 32 – 8 + 6
               = 30

Find
Find




       = 2(4x2 – 4x + 1) + 2x – 1 – 1
Graphs of polynomial functions


                                 Example:
                                 f(x) = 4
Example:
f(x) = 2x + 3
Example:
f(x) = x2 – 2
Example:
f(x) = x3 + 2x
Example:
f(x) = x4 + 2x3 + 5
Example:
f(x) = x5 + 3x3 + 5x
Even-degree
 functions
If leading
End behavior?                   coefficient is
Ends move in                    negative, left
   opposite                    side will be up.
directions (one
up, one down)




                  Odd-degree
                   functions
Even-degree
                  functions




End behavior?                     If leading
                                coefficient is
Ends move in                   negative, both
same direction                  sides will be
                                     down
For the graph:
 Does it represent an odd-
degree or an even-degree
function? EVEN

 State the number of real
zeros NONE

Describe the end behavior
For the graph:
 Does it represent an odd-
degree or an even-degree
function? ODD

 State the number of real
zeros 3

Describe the end behavior
For the graph:
 Does it represent an odd-
degree or an even-degree
function? EVEN

 State the number of real
zeros two

Describe the end behavior

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Alg2 lesson 7-1

  • 1. The degree of a polynomial in one variable is the greatest exponent of its variable. The leading coefficient is the coefficient of the term with the greatest degree. Is the expression a polynomial in one variable? If it is, state the degree and leading coefficient. Yes; degree: 4 leading coefficient: 1 No; It contains two variables, a and b. No; The term 2c–1 is not a monomial (dividing by the variable c).
  • 2. Find 2 2 2 2 2 = 32 – 8 + 6 = 30 Find
  • 3. Find = 2(4x2 – 4x + 1) + 2x – 1 – 1
  • 4. Graphs of polynomial functions Example: f(x) = 4
  • 8. Example: f(x) = x4 + 2x3 + 5
  • 9. Example: f(x) = x5 + 3x3 + 5x
  • 11. If leading End behavior? coefficient is Ends move in negative, left opposite side will be up. directions (one up, one down) Odd-degree functions
  • 12. Even-degree functions End behavior? If leading coefficient is Ends move in negative, both same direction sides will be down
  • 13. For the graph: Does it represent an odd- degree or an even-degree function? EVEN State the number of real zeros NONE Describe the end behavior
  • 14. For the graph: Does it represent an odd- degree or an even-degree function? ODD State the number of real zeros 3 Describe the end behavior
  • 15. For the graph: Does it represent an odd- degree or an even-degree function? EVEN State the number of real zeros two Describe the end behavior