Rational Zero Theorem (Algebra 2)

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Using the Rational Zero Theorem, list all of the possible rational zeros for each function.

1. h(x) = 2x^3 + 5x^2 - 8x - 10

2. f(x) = 3x^4 + 15

Thank you so much!

Feb 4th, 2015

1.)   h(x) = 2x^3 + 5x^2 - 8x - 10.

                List the factors (positive and negative) of the constant term (term with no variable next to it).

                          Constant term is -10 --->   +/- 1, +/- 2, +/-5, +/- 10

                 List the factors (positive and negative) of the leading coefficient

                           Leading Coefficient is 2 --->  +/- 1, +/- 2

                 Divide each factor of the constant term by each factor of the leading coefficient to get all of your possible rational zeroes.

                          (+/- 1) / (+/- 1) = +/- 1

                          (+/- 1) / (+/- 2) = +/- 1/2

                          (+/- 2) / (+/- 1) = +/- 2

                          (+/- 2) / (+/- 2) = +/- 1

                          (+/- 5) / (+/- 1) = +/- 5

                          (+/- 5) / (+/- 2) = +/-  5/2

                          (+/- 10) / (+/- 1) = +/- 10

                          (+/- 10) / (+/- 2) = +/- 5

                  List all of your results (try not to write repeats).  These would be your possible rational zeroes

                          +/- 1, +/- 1/2,  +/- 2, +/-5,  +/- 5/2,  +/- 10

                  We can also write them like this:

                           1, -1, 1/2, -1/2, 2, -2, 5, -5, 5/2, -5/2, 10, -10


                SOLUTION:    1,   -1,   1/2,   -1/2,   2,   -2,   5,   -5,   5/2,   -5/2,   10,   -10




2.)   3x^4 + 15

               Constant term is 15  --->    +/- 1, +/- 3, +/- 5, +/- 15

               Leading Coefficient is 3  --->  +/- 1, +/- 3

                (+/- 1) / (+/- 1) = +/- 1

                (+/- 1) / (+/- 3) = +/-  1/3

                (+/- 3) / (+/- 1) = +/- 3

                (+/- 3) / (+/- 3) = +/- 1

                (+/- 5) / (+/- 1) = +/- 5

                (+/- 5) / (+/- 3) = +/- 5/3

               (+/- 15) / (+/- 1) = +/- 15

               (+/- 15) / (+/- 3) = +/- 5

                   Rational zeroes:   +/- 1, +/- 1/3, +/- 3  +/- 5,  +/- 5/3,  +/- 15


           SOLUTION:  1,  -1,  1/3,  -1/3,  3,  -3,  5,  -5,  5/3,  -5/3,  15,  -15

Feb 4th, 2015

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