Question

Use the zero property product to find the solutions to the equation x^2-9= 16

1) x=-3 or x=3
2) x=-6 or x=-3
3) x=-5 or x=5
4) x=7 or x=1

Answer 1

Subtract 16 to get
  x^2 -25 = 0
Factor this as
  (x -5)(x +5) = 0

The zero product property tells you the product will be zero when one of the factors is zero.

For x-5 = 0
  x = 5

For x+5 = 0
  x = -5

The appropriate choice is
  3) x=-5 or x=5