Polynomials, Factoring

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

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

Multiply the Polynomials:

(x - 1)(−8x² − 6x − 12 )

-8x³ + 2x² - 6x + 12

Factoring whena is 1

100

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

What is 16?

200

The result of factoring:
x² + 8x + 12 

What is
(x + 2)(x + 6)?

300

The result of factoring:
x² - 6x + 8

What is
(x - 4)(x - 2)?

400

The result of factoring:
x² - 10x - 24 

What is
(x - 12)(x + 2)?

500

The result of factoring:
x² + 4x + 4 

What is
(x + 2)²?

Factoring when a is not 1

100

The result of factoring:
3x² + 20x + 12

What is
(3x+2)(x+6)?

200

The result of factoring:
3x² - 19x - 14 

What is
(3x + 2)(x - 7)?

300

The result of factoring:
4x² + 24x + 32

What is
4(x + 2)(x + 4)?

400

The results of factoring:
8x² + 18x + 9

What is
(4x + 3)(2x + 3)?

500

The result of factoring:
16x² - 8x + 1

What is
(4x - 1)²?

Factoring Special Polynomials

100

Factor fully: x²-9

(x-3)(x+3)

200

Factor fully: 4x²+12x+9

(2x+3)² or (2x+3)(2x+3)

300

Factor fully: x⁴-625

(x-5)(x+5)(x²+25)

400

Factor fully: 9x²-12x+4

(3x-2)² or (3x-2)(3x-2)

500

Factor fully: x¹⁶-1

(x-1)(x+1)(x²+1)(x⁴+1)(x⁸+1)