Operations w/Polynomials

Adding and Subtracting Polynomials

100

Add the Polynomials

(4x + 9) + (x - 4)

5x + 5

200

Add the polynomials:

(x² +3x + 5) + ( x² +6x)

2x² + 9x + 5

300

DOUBLE POINT QUESTION! 

Subtract the Polynomials:

(2x² - 3x +11 ) - (x² -2x + 4)

x² - x + 7

400

Subtract the Polynomials:

(k² + 6k³ -4) - (5k³ + 7k -3k²)

k³ + 4k² -7k -4

500

Add the polynomials:

(-1 + x² + 2x) + (1 -2x + 2x²)

3x²

Multiplying Polynomials

100

Multiply the Polynomials:

(x - 3)(x + 2)

x² - x - 6

200

Multiply the Polynomials:

(4n - 1)(3n + 4)

12n² + 13n - 4

300

Multiply the Polynomials.

(2x - 6)²

4x² - 24x + 36

400

Multiply the Polynomials:

(x+5)(2x²-5x+8)

2x³+5x²-17x+40

500

DOUBLE POINT QUESTION! 

Multiply the Polynomials:

(x - 1)(−8x² − 6x − 12 )

-8x³ + 2x² - 6x + 12

Factoring whenleading coefficient = 1

100

To factor the trinomial x²+8x+16 you find two numbers that add to 8 but multiply to this...

16

200

Factor:
x² + 8x + 12 

(x + 2)(x + 6)

300

Factor: 
x² - 6x + 8

(x - 4)(x - 2)

400

DOUBLE POINT QUESTION! 

Factor and solve:
x² - 10x - 24 

(x - 12)(x + 2); 

x = 12, x = -2

500

Factor and solve: 
x² + 4x + 4 

(x + 2)²

x = -2

Factoring when leading coefficient > 1

100

Factor: 
3x² + 20x + 12

(3x+2)(x+6)

200

DOUBLE POINT QUESTION! 

Factor:
3x² - 19x - 14 

(3x + 2)(x - 7)

300

DOUBLE POINT QUESTION! 

Factor COMPLETELY
4x² + 24x + 32

4(x + 2)(x + 4)

400

Factor: 
8x² + 18x + 9

(4x + 3)(2x + 3)

500

Factor and solve:
16x² - 8x + 1

*Surprise bonus...

(4x - 1)²

x= 1/4 

*If you get this question correct, you can steal 200 points from another group.

Special Products

100

DOUBLE POINT QUESTION! 

Factor:
x² + 6x + 9

(x+3)²

200

Factor: 
16x² - 9

(4x + 3)(4x - 3)

300

Factor: 
9x² + 6x + 1

(3x+1)²

400

Factor and solve:
81x² - 49

*Surprise bonus...

(9x - 7)(9x + 7)

x = 7/9 or -7/9

*If you get this question correct, you can steal 200 points from another group.

500

Factor and solve: 
4x² - 20x + 25

(2x-5)²

x= 5/2 (or 2 1/2)