Imaginary numbers and dividing polynomials

Complex Numbers

100

What two parts make up a complex number?

Real Part and Imaginary Part

200

How do we add complex numbers?

Add real to real and imaginary to imaginary

300

Add the following:

`(4+2i)+(-2+3i)`

2+5i

400

Subtract the following:

`(5+3i)-(3+3i)`

2

500

Multiply the following:

`(4-3i)(4+3i)`

25

Imaginary Numbers

100

What is the following equal to? 

`i^2`

-1

200

Rewrite the following with an imaginary number

4i

300

Multiply the following 

`(3i)(2i)`

-6

400

Evaluate the following 

`(5i^2) (3i^2)`

15

500

What does this equal to? 

`i^8`

1

Graphing Polynomials

100

Will this graph cross or bounce off the x-axis?

`y=x^2`

bounce

200

State the degree of the polynomial 

`y=(x-3)^2(x-4)^3(x-5)`

6

300

State the leading coefficient and whether your graph is positive or negative orientation.

`y=3x^2-5x^4+2x-4`

-5

Negative orientation

400

State the degree and whether the ends with face the same or opposite directions:

`y=3x^2-5x^4+2x-4`

degree: 4

Same direction

500

`y=x(x-2)^2(x-4)^3`

Sketch a quick graph of the following polynomial:

Dividing Polynomials

100

How would you set up the following division problem using the long division method:

`(9x)/3`

200

Divide the following expression:

`(18x)/2`

9x

300

What goes in the missing square?

`2x^3`

400

Solve the following expression: 

`(x^2+2x-15)/(x+5`

(x-3)

500

Divide the following: 

`(x^3-4x^2+6x-4)/(x-2)`

`x^2-2x+2`

x-intercepts and roots

100

What is y-value for any x-intercept?

y=0

200

State the x-intercepts of the following polynomial.

`y=(x+2)(x-4)`

x=-2

x=4

300

State the roots of the following polynomial

`y=x(x^2-25)`

x=0

x=5

x=-5

400

How many times with this graph touch the x-axis? 

`y=(x^2+36)(x-2)(x+4)`

two times at 

x=2

x=-4

500

State the roots:

`y=(x^2+9)(x^2-16)`

x=4

x=-4

x=-3i

x=3i