Polynomials

Factoring Polynomials

100

x² -7x - 18

(x+2)(x-9)

200

a²-15a+36

(a-3)(a-12)

300

b² - 81

(b+9)(b - 9)

400

2x²+6x+4

2(x+2)(x+1)

500

3x⁴-31x³+10x²

x²(3x -1)(x - 10)

Adding Polynomials

100

Write answer in standard form

(5p² −3)+(2p² −3p³ )

-3p³ +7p² −3

200

(5a²+ 4a - 6) + (2a² - 5a + 7)

7a² - 1x + 1

300

(7x² - 6x + 18) + (4x² + 12x - 11)

11x² +6x + 7

400

(−7x⁵ +14 − 2x)+(10⁴x + 7x + 5x⁵ )

−2x⁵ + 10x⁴ +5x + 14

500

If the length of a rectangle in terms of x is 9x² + x – 5, and its width is 3x²+ 4x + 4, what is the perimeter of this rectangle? Don’t leave any spaces in your solutions.

P = 2l + 2w

P = 2(9x² + x – 5) + 2(3x² + 4x + 4)

= 18x² + 2x – 10 + 6x² + 8x + 8

= 24x² + 10x - 2

= 2(12x² + 5x - 1)

Subtracting Polynomials

100

(6x² + 4x + 1) – (4x + 20)

6x²– 19

200

(–7x⁹ + 12x⁶– 12) – (5x⁹ + 4x⁶– 9)

-12x⁹+8x⁶-3

300

(a³–2a²)–(3a²–4a³)

5a³–5a²

400

(3x⁴–3x + 7x²)–(3x– 8 - 3x⁴ )

6x⁴ + 7x² - 6x + 8

500

(12a⁵ − 6a − 10a³) − (10a − 2a⁵ − 14a⁴)

14a⁵ + 14a⁴ − 10a³− 16a

Multiplying Polynomials

100

6v(2v + 3)

12v² + 18v

200

(2n+7)²

4n² +28n+49

300

(6p+8)(5p−8)

30p² − 8p − 64

400

(3x−4)(4x+3)

12x² −7x−12

500

(m² −7m−6)(7m² −3m−7)

7m⁴ −52m³ −28m² +67m+42

Dividing Polynomials

100

(12n²– 18n – 24) ÷ (6)

2n² -3n - 4

200

9x⁵ +9x⁴+45x³/9x²

x³+x²+5x

300

3v³+v²+2v/9v³

1/3+1/9v+2/9v²

400

(3k⁴ – 18k³ – 42k²) ÷ (3k)

k³ – 6k² - 14k

500

(60p³+150p²+15p) ÷ 15p

4p²+10p+1