Question

The product of two consecutive even integers is equal to 48. translate into an equation and solve for factors.

Answer 1

Let one of the number be x.
The other number will be x + 2.

The product of the two numbers is 48.
⇒ x(x + 2) = 48

x(x + 2) = 48
x² + 2x = 48
x² + 2x - 48 = 0
(x - 6) (x + 8) = 0

x = 6 or x = -8

When x = 6
The integers are 6 and 8

When x = -8
The integers are -8 and -6

Answer: The numbers are 6 and 8 or -6 and -8.

Answer 2

If n is an even integer:
n(n + 2) = 48
n^2 + 2n - 48 = 0
(n + 8)(n - 6) = 0
n = -8 or n = 6