Polynomial Functions
Real Zeros
Rational Functions
Complex Numbers
The Fundamental Theorem of Algebra
100
A constant polynomial that consists of only a constant term, such as the polynomial 12 is called...
constant polynomial
100

Describe how to find all possible rational zeros.

Rational zero test.

Factors of constant divided by the factors of leading coefficient.

100
What is domain?
All x values that are not zeros of denominator.
100
What is standard form of complex numbers?
a+bi
100

Find a possible polynomial in factored form such that 1(with multiplicity 3), -2, and 5 are zeros.

`f(x)=(x-1)^3(x+2)(x-5)`

200

What is the leading coefficient of

`6x^7+4x^3+5x^2-7x+10`

6

200

Find the zeros of the following function.

`f(x) = 3x^2(x-4)(x^2-4)(2x+5)`

`0, 4, +-2, -5/2`

200
All x-values that are zeros of numerator but not zeros of the denominator.
What is intercepts?
200
What is the conjugate of 2+3i
2-3i
200

Find zeros:

`f(x)=x^2-6x+13`

The zeros are: 3+2i and 3-2i

300

Use synthetic division to divide

`x^5+5x^4+6x^3-x^2+4x=29`

 by x+3

`x^4+2x^3-x+7`

300

Find rational zeros of 

`f(x)=2x^4+x^3-17x^2-4x+6`

`-3, 1/2`

300
All x-values where the denominator is zero but the numerator is not zero.
What is vertical asymptotes?
300
Write (1+i)+(3-7i) in a+bi form.
4-6i
300

Find a polynomial with zeros at 2 and 3+i.

`f(x)=x^3-8x^2+22x-20`

400
If multiplicity is odd, the graph crosses what axis?
x-axis
400

Find all zeros given that -4 is a zero.

`f(x)= x^4+x^3-14x^2-2x+24`

`+- sqrt(2) , 3, -4`

400

Find vertical asymptotes:

`(x^2+2x+1)/(x^2-x-6)`

`x = 3 and x= -2`

400

Find 

`i^54`

-1

400

Find the possible rational zeros of

`f(x)=x^4-5x^3+4x^2+2x-8`

 over the set of real numbers.

The possible rational zeros are factors of 8. 

`+-1, +-2, +-4, +-8`

500
If multiplicity is even, what does the graph do?
Touches, does not cross the x-axis
500

Find all real zeros

`f(x)=x^3-3x^2+2x-6`

3

500

Find x and y intercepts:

`f(x)=(x^2-x-2)/(x-1)`

x intercept: x=2 and -1 y intercept: y=2

500

Put

`(3+4i)/(1+2i)`

 in a+bi form.

`11/5- 2/5i`

500

Completely factor

`f(x)=x^4-5x^3+4x^2+2x-8`

over the set of complex numbers.

The complex factors are: x-(1+i) and x-(1-i)