##### Rational Zero Theorem (Algebra 2)

 Algebra Tutor: None Selected Time limit: 1 Day

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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Feb 4th, 2015
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Feb 4th, 2015
Dec 10th, 2016
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