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Polynomial Functions
       Section 5.1
The degree of a polynomial is the greatest exponent
of the variable.

    3x - x + 6
       2
The degree of a polynomial is the greatest exponent
of the variable.

    3x - x + 6
       2
The degree of a polynomial is the greatest exponent
of the variable.

    3x - x + 6
       2    1
The degree of a polynomial is the greatest exponent
of the variable.

    3x - x + 6
       2    1




                Degree        Name of polynomial

                  0                Constant
                  1                 Linear
                  2               Quadratic
                  3                 Cubic
                  4                Quartic
                  5                Quintic
The degree of a polynomial is the greatest exponent
of the variable.
                             Degree 2 polynomial
    3x - x + 6
       2    1
                             -quadratic

                Degree        Name of polynomial

                  0                Constant
                  1                 Linear
                  2               Quadratic
                  3                 Cubic
                  4                Quartic
                  5                Quintic
The                                       arranges
the terms by degree in descending numerical order.


       3x 3 - 5+ x - 4x 4
The                                       arranges
the terms by degree in descending numerical order.


       3x 3 - 5+ x - 4x 4
The                                       arranges
the terms by degree in descending numerical order.


       3x - 5+ x - 4x 4
         3      1
The                                       arranges
the terms by degree in descending numerical order.

                                      Signs in front of
       3x - 5+ x - 4x
         3      1       4
                                     terms go with the
                                           term.



                            -4x 4
The                                       arranges
the terms by degree in descending numerical order.

                                      Signs in front of
       3x - 5+ x - 4x
         3      1       4
                                     terms go with the
                                           term.



                     -4x 4 + 3x 3
The                                       arranges
the terms by degree in descending numerical order.

                                        Signs in front of
       3x - 5+ x - 4x
         3      1       4
                                       terms go with the
                                             term.



                    -4x 4 + 3x 3 + x
The                                       arranges
the terms by degree in descending numerical order.

                                            Signs in front of
       3x - 5+ x - 4x
         3      1       4
                                           terms go with the
                                                 term.



                    -4x 4 + 3x 3 + x - 5
The                                       arranges
the terms by degree in descending numerical order.

                                              Signs in front of
       3x - 5+ x - 4x
          3       1       4
                                             terms go with the
                                                   term.



                      -4x 4 + 3x 3 + x - 5


   A                 is the coefficient of the first term
   when the polynomial is in standard form. It has
   important use!
The                                       arranges
the terms by degree in descending numerical order.

                                              Signs in front of
       3x - 5+ x - 4x
          3       1       4
                                             terms go with the
                                                   term.



                      -4x 4 + 3x 3 + x - 5


   A                 is the coefficient of the first term
   when the polynomial is in standard form. It has
   important use!
Write each polynomial in standard form. Then classify it by degree and state the leading
coefficient.


   1. 4x3     3+                       2. 3 + 24x2                  3. 6x + 2x4   2
   2x2




   4. 8     x5 + 9x2   2x              5. -13 + x                   6. 8
Write each polynomial in standard form. Then classify it by degree and state the leading
coefficient.


   1. 4x3     3+                       2. 3 + 24x2                  3. 6x + 2x4   2
   2x2
            4x3 + 2x2 3
            Cubic
            L.C. 4




   4. 8     x5 + 9x2   2x              5. -13 + x                   6. 8
Write each polynomial in standard form. Then classify it by degree and state the leading
coefficient.


   1. 4x3     3+                       2. 3 + 24x2                  3. 6x + 2x4   2
   2x2
            4x3 + 2x2 3                     24x2 + 3                       2x4 + 6x    2
            Cubic                           Quadratic                      Quartic
            L.C. 4                          L.C. 24                        L.C. 2




   4. 8     x5 + 9x2     2x            5. -13 + x                   6. 8

              x5 + 9x2    2x + 8             x – 13                        8
            Quintic                         Linear                         Constant
            L.C. -1                         L.C. 1                         L.C. None
Graph each function using the domain x = -2, -1, 0, 1, 2, 3.
          y = x 3 - 3x



                                               x     y
                                               -2    -2
                                               -1    2
                                               0     0
                                               1     -2
                                               2     2
                                               3     18
Graph each function using the domain x = -2, -1, 0, 1, 2, 3.
       y = x 4 - 3x 3 + 5x

                                               x     y
                                              -2    30
                                              -1     -1
                                               0     0
                                               1     3
                                               2     2
                                               3    15

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Algebra 2: 5.1 Classn Notes

  • 1. Polynomial Functions Section 5.1
  • 2. The degree of a polynomial is the greatest exponent of the variable. 3x - x + 6 2
  • 3. The degree of a polynomial is the greatest exponent of the variable. 3x - x + 6 2
  • 4. The degree of a polynomial is the greatest exponent of the variable. 3x - x + 6 2 1
  • 5. The degree of a polynomial is the greatest exponent of the variable. 3x - x + 6 2 1 Degree Name of polynomial 0 Constant 1 Linear 2 Quadratic 3 Cubic 4 Quartic 5 Quintic
  • 6. The degree of a polynomial is the greatest exponent of the variable. Degree 2 polynomial 3x - x + 6 2 1 -quadratic Degree Name of polynomial 0 Constant 1 Linear 2 Quadratic 3 Cubic 4 Quartic 5 Quintic
  • 7. The arranges the terms by degree in descending numerical order. 3x 3 - 5+ x - 4x 4
  • 8. The arranges the terms by degree in descending numerical order. 3x 3 - 5+ x - 4x 4
  • 9. The arranges the terms by degree in descending numerical order. 3x - 5+ x - 4x 4 3 1
  • 10. The arranges the terms by degree in descending numerical order. Signs in front of 3x - 5+ x - 4x 3 1 4 terms go with the term. -4x 4
  • 11. The arranges the terms by degree in descending numerical order. Signs in front of 3x - 5+ x - 4x 3 1 4 terms go with the term. -4x 4 + 3x 3
  • 12. The arranges the terms by degree in descending numerical order. Signs in front of 3x - 5+ x - 4x 3 1 4 terms go with the term. -4x 4 + 3x 3 + x
  • 13. The arranges the terms by degree in descending numerical order. Signs in front of 3x - 5+ x - 4x 3 1 4 terms go with the term. -4x 4 + 3x 3 + x - 5
  • 14. The arranges the terms by degree in descending numerical order. Signs in front of 3x - 5+ x - 4x 3 1 4 terms go with the term. -4x 4 + 3x 3 + x - 5 A is the coefficient of the first term when the polynomial is in standard form. It has important use!
  • 15. The arranges the terms by degree in descending numerical order. Signs in front of 3x - 5+ x - 4x 3 1 4 terms go with the term. -4x 4 + 3x 3 + x - 5 A is the coefficient of the first term when the polynomial is in standard form. It has important use!
  • 16. Write each polynomial in standard form. Then classify it by degree and state the leading coefficient. 1. 4x3 3+ 2. 3 + 24x2 3. 6x + 2x4 2 2x2 4. 8 x5 + 9x2 2x 5. -13 + x 6. 8
  • 17. Write each polynomial in standard form. Then classify it by degree and state the leading coefficient. 1. 4x3 3+ 2. 3 + 24x2 3. 6x + 2x4 2 2x2 4x3 + 2x2 3 Cubic L.C. 4 4. 8 x5 + 9x2 2x 5. -13 + x 6. 8
  • 18. Write each polynomial in standard form. Then classify it by degree and state the leading coefficient. 1. 4x3 3+ 2. 3 + 24x2 3. 6x + 2x4 2 2x2 4x3 + 2x2 3 24x2 + 3 2x4 + 6x 2 Cubic Quadratic Quartic L.C. 4 L.C. 24 L.C. 2 4. 8 x5 + 9x2 2x 5. -13 + x 6. 8 x5 + 9x2 2x + 8 x – 13 8 Quintic Linear Constant L.C. -1 L.C. 1 L.C. None
  • 19. Graph each function using the domain x = -2, -1, 0, 1, 2, 3. y = x 3 - 3x x y -2 -2 -1 2 0 0 1 -2 2 2 3 18
  • 20. Graph each function using the domain x = -2, -1, 0, 1, 2, 3. y = x 4 - 3x 3 + 5x x y -2 30 -1 -1 0 0 1 3 2 2 3 15