Polynomials and Quadratics

Adding Polynomials

100

(2+ 5p⁴) + (3p⁴ + 2)

8p⁴ + 4

200

(5k - 4k³) + (5k + 5k³ - 1)

k³ + 10k - 1

300

(x³-2x⁴-5x²)+(3x⁴ - 3x³) 

x⁴ - 2x³ - 5x²

400

(3k + 8 - 5k²) + (5k² + 4k⁴ + 7k + 2)

4k⁴ + 10k + 10

500

(x - 8x² + 6x⁴ + x³) + (2x² + 5x⁴ + 3x³ - 4x)

11x⁴ + 4x³ - 6x² - 3x

Subtracting Polynomials

100

(2x + 4x⁴) - (x + 3x⁴)

x⁴ + x

200

(5a² - 2a³) - (3a² - 4a³ + 3a⁴)

-3a⁴ + 2a³ + 2a²

300

(2n⁴ + n³ + 2n) - (n - 2n³)

2n⁴ + 3n³ + n

400

(n³ + 3n⁴ - 3) - (n⁴ + 4 - 3n²)

2n⁴ + n³ + 3n² - 7

500

(3n² + 5n⁴ - 1) - (3n² + 1 + 3n⁴)

2n⁴ - 1

Multiplying Polynomials

100

4x (2x⁴)(3x⁴)

24x⁹

200

5a²(4a⁵)(5a⁰)

100a⁷

300

8m²(-5m + 4)

-40m³ + 32m²

400

-5p³(-2p - 4)

10p⁴ +20p³

500

-4p(-p + 4)

4p² - 16p

FOIL Method

100

(n+4)²

n² + 8n + 16

200

(p + 5) (p - 5)

p² - 25

300

(a + 2) (6a + 2)

6a² + 14a + 4

400

(6x + 1)2²

36x² + 12x + 1

500

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

9x² - 25

Factoring Trinomials

100

k² - 7k + 10

(k - 2) (k - 5)

200

v² + 9v + 18

(v+3) (v+6)

300

v² - 7v - 8

(v + 1) (v - 8)

400

6m² - 24m - 72

6(m + 2) (m - 6)

500

4m² - 72m + 320

4(m - 8) (m - 10)