__2.3 Real Zeros of Polynomial Functions__

__Polynomial Function__: F(x)=

To find real zeros of polynomial functions you can:

**1. Divide by known factors (synthetic division/quadratic formula)**

- If x-a is a factor, factor it out of the equation by using synthetic division

- If the remainder is zero, then the number is a factor

Example #1:

Is x- a factor of -2x+3

Yes, x- is a factor of -2x+3

- after factoring out x-, keep factoring until simplified

- solve the problem to find the zeros

Link to see more examples:

http://id.mind.net/~zona/mmts/functionInstitute/polynomialFunctions/roots/syntheticDivision.html

**2. Rational Root Therom **

__Rational Root Therom__: All possible rational roots are of the for .

p-- factors of last tern of the polynomial function

q-- factors of the first term of the polynomial function

Example #2:

Find all possible rational roots in the equation F(x)=

1 + 12

p-- 1, 2, 3, 4, 6, 12

q-- 1

**= –12, –6, –4, –3, –2, –1, 1, 2, 3, 4, 6, 12**

For further explination visit __http://www.purplemath.com/modules/rtnlroot2.htm__

**3. Graph**

- Plug in the equation to the calculator

Example #3: Graph f(x)=

*x* = -2, 1, 3

-zeros cross the x-axis

-to find zeros using calculator second trace (calc) zero

Example #4: Graph f(x)=

x= -1, 2

**Now it's your turn!**

Is (x-1) a factor of the following?

1. f(x) = x^{4} - 2x^{3} + x - 2

2. f(x) = x^{3} + 2x^{2} - 3x + 1

Use the Rational Root Therom to find out the rational roots.

1. f(x) = x^{4} - 2x^{3} + x - 2

2. f(x) = x^{3} + 2x^{2} - 3x + 1

Graph the polynomial functions.

1. f(x) = x^{4} - 2x^{3} + x - 2

2. f(x) = x^{3} + 2x^{2} - 3x + 1

Link to the polynomial function zero video:

__http://videos.howstuffworks.com/hsw/11298-polynomial-functions-the-zero-property-video.htm__

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