Polynomials - Factoring, Finding Zeros, Writing Equations

Factoring

100

Factor: x² + 6x - 27.

(x - 3)(x + 9)?

200

Factor: 2x³ + 36x² +160x.

2x(x + 8)(x + 10)?

300

Factor: 16x³ - 2x² + 56x - 7.

(2x² + 7)(8x - 1)?

400

Factor: 250x³ + 432

2(5x + 6)(25x² - 30x + 36)?

500

Factor: 20x⁸ - 21x⁴ + 4

(2x² - 1)(2x² + 1)(5x⁴ - 4)

Writing a Polynomial Function

100

The standard form polynomial function with zeros 4, 0, 1.

f(x) = x³ - 5x² + 4x

200

The standard form polynomial function with zeros -2, 2, 3.

f(x) = x³ - 3x² - 4x + 12

300

The standard form polynomial function with zeros 1, 2, 5/4.

f(x) = 4x³ - 17x² + 23x - 10

400

The standard form polynomial function with zeros -4/3, -1/5, 2/5.

f(x) = 75x³ + 85x² - 26x - 8

500

The standard form polynomial function with zeros -3/5, -2i.

f(x) = 5x³ + 3x² + 20x + 12

Finding Zeros by Factoring

100

Is (x-2) a factor of P(x) = x³ + 2x² -6x - 4? Show why or why not.

Yes; P(x) = (x - 2)(x² + 4x + 2)

200

Find all zeros:

f(x) = x³ + 7x² + 10x.

{0, -2, -5}

300

Find all zeros:

 f(x) = x⁴ - 40x² + 144.

{-6, 6, -2, 2}

400

Find all zeros:

f(x) = 2x³ - 3x² - 3x + 2

{-1, 1/2, 2}

500

Find all zeros:

f(x) = 4x³ - 3x² - 8x + 6

3/4, +- radical 2

Finding Zeros

100

Find all zeros: 

f(x) = 2x⁴ + 3x² + 1

-1/5, -1, -1

200

Find all zeros:

f(x) = x³ - 2x² + 10x + 136 

{-4, 3+5¡, 3-5¡}

300

Find all zeros: 

f(x)= x³ - 216

{6, -3+3¡√3, -3-3¡√3}

400

Find all zeros:

f(x) = -x³ - x² - 7x - 7 

{¡√7, -¡√7, -1}

500

Find all the zeros: 

f(x) = 2x³ + 2x² - 19x + 20

{3+¡/2, 3-¡/2, -4}

Synthetic Substitution

100

f(x) = x³ - 5x² + 6x - 6; find f(3) 

f(3) = -6

200

f(x) = x³ - 5x + 5; find f(2)

f(2) = 3

300

f(x) = -2x³ + 17x² - 33x + 30; find f(6)

f(6) = 12

400

f(x) = x⁴ + 3x³ - 8x - 16; find f(-2)

f(-2) = -8

500

f(x) = -5x⁵ + 26x⁴ -9x³ + 20x² + 5x - 17; find f(5)

f(5) = 8