Polynomial Functions

Polynomial Functions

100

Find the end behavior of -7x^3 + 8x^2 + x.

up and down

200

Classify 3 + 12x^4 by degree.

Quartic

300

Classify 7x + 3x + 5 by number of terms.

Binomial

400

Write (2a - 5)(a^2 - 1) in standard form. Then classify by degree and number of terms.

2a^3 - 5a^2 - 2a + 5 Cubic Polynomial of 4 terms

500

Find the degree of the polynomial function: x y 5 10 6 17.28 7 27.44 8 40.96 9 58.32

Cubic

Factoring

100

Factor: x^3 + 7x^2 + 10x

x(x + 5)(x + 2)

200

Factor: x^3 - 7x^2 _ 18x

x(x - 9)(x + 2)

300

Factor: x^3 - 36x

x(x - 6)(x + 6)

400

Factor: 9x^3 + 6x^2 - 3x

3x(x + 1)(3x - 1)

500

Given x = -2, 0, 1, write the polynomial equation.

x^3 + x^2 - 2x = 0

Zeros of a Function

100

Find the zeros: y = (x - 1)(x + 2)

x = 1, x = -2

200

Find the zeros: y = x (x - 1)^3

x = 0, x = 1

300

Find the zeros and state the multiplicity of y = (2x + 3)(x - 1)^2.

x = -3/2, multiplicity of 1 x = 1, multiplicity of 2

400

Find the zeros and state the multiplicity of y = 3x^3 - 3x.

x = 0, multiplicity of 1 x = 1, multiplicity of 1 x = -1, multiplicity of 1

500

Find the zeros and state the multiplicity of y = 2x^3 + x^2 - x.

x = 0, multiplicity of 1 x = -1, multiplicity of 1 x = 1/2, multiplicity of 1

Solving

100

Solve x^3 + 13x = 10x^2

x = 0, x = (5 + 2square root of 3)/2 x = (5 - 2square root of 3)/2

200

Solve 12x^3 = 60x^2 + 75x

x = 0 x = (5 + 5square root of 2)/2 x = (5 - 5square root of 2)/2

300

Solve 27 = -x^4 - 12x^2

x = 3i x = -3i x = i square root of 3 x = -i square root of 3

400

Solve 125x^3 + 216 = 0

x = -6/5 x = (3 + 3i square root of 3)/5 x = (3 - 3i square root of 3)/5

500

Solve x^3 + 1 = x^2 + x

x = 1 x = -1

Dividing

100

(x^3 + 3x^2 - x - 3) / (x -1)

x^2 + 4x + 3

200

(x^3 - 4x^2 + 6x - 4) / (x -2)

x^2 - 2x + 2

300

(x^3 + 27) / (x + 3)

x^2 - 3x + 9

400

Find P(a). P(x) = x^3 + 4x^2 - 8x - 6; a = -2

18

500

Factor Completely: (x^3 + 2x^2 - 5x - 6) / (x + 1)

(x + 1)(x + 3)(x - 2)