How many roots does the polynomial function, y = (x + 4) (x-2) (x+7) have?

A. 3

B. 1

C. 2

D. A

A. 3

Step-by-step explanation:

The polynomial y = (x + 4) (x - 2) (x + 7) has 3 roots.

y = 0 ⇒ (x + 4) (x - 2) (x + 7) = 0 ⇔ x + 4 = 0 ∨ x - 2 = 0 ∨ x + 7 = 0

x + 4 = 0 subtract 4 from both sides

x = - 4

x - 2 = 0 add 2 to both sides

x = 2

x + 7 = 0 subtract 7 from both sides

x = - 7