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# Real-Zeros-of-Polynomial-Functions

last edited by 11 years, 11 months ago

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

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

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

1. f(x) = x4 - 2x3 + x - 2

2. f(x) = x3 + 2x2 - 3x + 1

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

1. f(x) = x4 - 2x3 + x - 2

2. f(x) = x3 + 2x2 - 3x + 1

Graph the polynomial functions.

1. f(x) = x4 - 2x3 + x - 2

2. f(x) = x3 + 2x2 - 3x + 1

Link to the polynomial function zero video:

http://videos.howstuffworks.com/hsw/11298-polynomial-functions-the-zero-property-video.htm