Polynomial Operations and Factoring

Polynomial operations (one operation)

100

Simplify:

(-3x^2+4x-9)+(2x^2-5x-2)

-x^2-x-11

200

Simplify:

(x^2-5x+1)(5x^2-6x-8)

5x^4-31x^3+27x^2+34x-8

300

Simplify:

(-9x^3+8x-3)-(6x^3+7x^2-5)

-15x^3-7x^2+8x+2

400

Simplify:

-4x^3y^2z(2x^3yz^2-3xyz)

-8x^6y^3z^3+12x^4y^3z^2

500

Simplify:

(18a^3b^4c^2+4a^7b^8c-2a^3b^2c)/(2a^3b^2c

9b^2c+2a^4b^6-1

Polynomial operations (multiple operations)

100

Simplify:

3x(x^2-8)-4x^3

-x^3-24x

200

Simplify:

5x^2-8x-(x-4)(2x+3)

3x^2-3x+12

300

Simplify: 

(9x^3+8x^2-9)-(4x^3+8x^2+2x-7)+(-5x^3+2x+1)

-1

400

Simplify:

(x+4)(5x-3)-(x+3)^2

4x^2+11x-21

500

Simplify: 

(30x^3-15x^2+80x)/(5x)-(2x-5)^2

2x^2+17x-9

Factoring trinomials

100

Factor completely:

x^2+4x-5

(x+5)(x-1)

200

Factor completely:

2x^2-x-3

(2x-3)(x+1)

300

Factor completely:

6x^2-21x-12

3(2x+1)(x-4)

400

Factor completely:

x^4-3x^2-4

(x+2)(x-2)(x^2+1)

500

Factor completely:

16x^4-52x^2+36

4(2x+3)(2x-3)(x+1)(x-1)

Factoring binomials

100

Factor completely:

x^2-25

(x+5)(x-5)

200

Factor completely:

8x^3+12x^2

4x^2(2x+3)

300

Factor completely:

-45x^2+500

-5(3x+10)(3x-10)

400

Factor completely:

-4x^3+49x

-x(2x+7)(2x-7)

500

Factor completely:

32x^4-162

2(4x^2+9)(2x+3)(2x-3)

Factoring 4 terms

100

Factor completely:

x^3-2x^2+3x-6

(x^2+3)(x-2)

200

Factor completely:

3x^3+2x^2-3x-2

(x+1)(x-1)(3x+2)

300

Factor completely:

4x^3+4x^2-9x-9

(2x+3)(2x-3)(x+1)

400

Factor completely:

10x^4+25x^3-30x^2-75x

5x(x^2-3)(2x+5)

500

Factor completely:

x^5+x^4-4x^3-4x^2

x^2(x+2)(x-2)(x+1)

Trivia

100

What is James Bond's code name?

007

200

What country is the largest in the world?

Russia

300

Which occasion corresponds to the longest day of the year?

Summer Solstice

400

How many states does the Appalachian Trail cross?

14

500

What is the only planet in our solar system to rotate clockwise on its axis?

Venus