Polynomials 8.1 - 8.5

Naming Polynomials

100

Name of a 2nd degree polynomial

Quadratic

200

Name of a 2 term polynomial

binomial

300

4x³

Cubic Monomial

400

4x + 2

Linear binomial

500

x² - 8x³ + 9x⁴ - 6

Quartic Polynomial

Adding/Subtracting Polynomials

100

(3x³ + 2x²) + (4x³ + 7x²)

7x³ + 9x²

200

(8z⁴ - 3z³ + z) + (7z³ + 2z⁴ - z)

10z⁴ + 4z³

300

(7n² + 10n) - (2n² + 3n)

5n² + 7n

400

(9n + 4 - 15n²) - (8n² + 5n - 10)

-23n² + 4n + 14

500

(8y⁵ + 3y³ - 10y) - (9y³ - 8y² - y⁴)

8y⁵ + y⁴ -6y³ +8y² -10y

Distributing Monomials

100

3x(x + 2)

3x² + 6x

200

8x(4x² - 2x)

32x³ - 16x²

300

10x³(5x⁴ + 9x³ - 3)

50x⁷ + 90x⁶ - 30x³

400

-7a²b(8a⁴b - 3a²)

-56a⁶b² + 21a²b

500

30x⁴y³z²(5x⁴y³z + x³y²z - 3xy)

150x⁸y⁶z³ + 30x⁷y⁵z³ - 90x⁵y⁴z²

FOIL

100

(x + 3)(x + 4)

x² + 7x + 12

200

(x + 9)(x - 2)

x² + 7x - 18

300

(5n + 9)(3n + 6)

15n² + 57n + 54

400

(7n² - 6)(2n - 3)

14n³ - 21n² - 12n + 18

500

(7x + 5)(7x² - 2x + 9)

49x³ + 21x² + 53x + 45

Factoring GCF

100

10x + 4

2(5x + 2)

200

8n² - 4n

4n(2n - 1)

300

15x⁴ + 25x³ - 20x²

5x²(3x² + 5x - 4)

400

40a⁴b⁷ - 84a⁴b⁵

4a⁴b⁵(10b² - 21)

500

110x⁹y⁶z³ - 55x⁷y⁵z + x⁵y⁴z

x⁵y⁴z(110x⁴y²z² - 55x² + 1)