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