Write a possible equation for a polynomial whose graph has the following horizonal intercepts. Show your work.

A. (4,0)

B. (0,0) and (4,0)

C. (-2,0), (0,0), and (4,0)

D. (-5,0), (1/2,0), and (3,0)

A) x - 4

B) x² - 4x

C) x³ - 2x² - 8x

D) 2x³ + 3x² - 32x + 15

Step-by-step explanation:

A)

x-intercepts: x = 4

Factors:

(x - 4)

B)

x-intercepts: x = 4, 0

Factor:

(x - 0) (x - 4)

x² - 4x

C)

x-intercepts: x = 4, 0, - 2

Factor:

(x - 0) (x - 4) (x + 2)

(x² - 4x) (x + 2)

x³ - 4x² + 2x² - 8x

x³ - 2x² - 8x

D)

x-intercepts: x = 3, ½, - 5

Factor:

(x - 3) (2x - 1) (x + 5)

(2x² - 6x - x + 3) (x + 5)

(2x² - 7x + 3) (x + 5)

2x³ - 7x² + 3x + 10x² - 35x + 15

2x³ + 3x² - 32x + 15