Polynomial Division and Complex Numbers

Long/Syn Division

100

Using long division, what is the divisor of this polynomial.

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

x²+2

200

Using Long Division, what is the quotient of this polynomial 

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

x+6

300

Using Synthetic Division, what is the quotient of this polynomial?

`(x^3+x^2+2x+9)/(x+2)`

`x^2-x+4`

400

Using Synthetic Division, what is the remainder of this polynomial?

`(3x^3-x^2+8x+7)/(x+2)`

-37

500

Using Synthetic Division, find the quotient of the polynomial.

`(2x^4+6x^3-10x^2-13x-29)/(x+4)`

Quotient: 

`2x^3-2x^2-2x-5`

Miscellaneous

100

Using Descarte's Rule of Signs, how many possible positive zeros are there?

`5x^5+10x`

0

200

Using Descarte's Rule of Signs, how many possible positive zeros are there?

`-5x^3+x^2-x+5`

3 or 1

300

Using Descarte's Rule of Signs, how many possible negative zeros are there?

`-5x^3+x^2-x+5`

0

400

List the possible rational zeros of the following polynomial (Hint these are the p's and q's):

`x^3+x^2+9x+9`

`p/q=1, 3, 9`

500

List the possible rational zeros of the following polynomial (Hint these are the p's and q's):

`5x^3-9x^2+28x+6`

`p/q=1, 1/5, 2, 2/5, 3, 3/5, 6, 6/5`

Complex Operations

100

Simplify 

`(2+3i)+(6-7i)`

`8-4i`

200

Simplify 

`(4-6i)-(-7+8i)`

`-11-14i`

300

Simplify

`2i(3+6i)-4(2-8i)`

`-20+38i`

400

Simplify:

`(2-6i)(3+4i)`

`30-10i`

500

Simplify:

`(4+2i)/(5+i)`

`11/13+3/13i`

Complex Conjugates

100

What is the complex conjugate of 3+5i

3-5i

200

What is the complex conjugate of -4-7i

-4+7i

300

What is the complex conjugate of 

`-4+sqrt(3)i`

`-4-sqrt(3)i`

400

What is the complex conjugate of 

`-2-2sqrt(2)i`

`-2+2sqrt(2)i`

500

What nationality is mathematician Rene Descartes?

French

Simplify

100

`sqrt(-16)`

4i

200

`sqrt(-48)`

`4sqrt(3)i`

300

`4i^2`

-4

400

4i²+6i³

-4-6i

500

`sqrt(-7)*sqrt(-8)`

`-2sqrt(14`