Question

One positive integer is 2 less than another. the product of the two integers is 24. what are the integers?

Answer 1

The numbers are 6 and 4

Explanation:

Let x = integer

The second is x-2

Product of x*(x-2) is 24

x(x-2) = 24

Distribute

x^2 -2x =24

Subtract 24 from each side

x^2 -2x -24 =24-24

x^2 -2x-24 =0

Factor

What two number multiply together to give 24 and add to -2

-6*4= -24

-6+4 = -2

(x-6) (x+4) =0

Using the zero product property

x-6 =0 x+4 = 0

x=6 x=-4

The question states the number is positive

x=6

The second number is x-2 = 4

The numbers are 6 and 4