Question

Ernie and Jacob were given some clues and challenged to find the product of three numbers. Ernie wrote the equation below.



8
x
3
+
36
x
2
+
46
x
+
15
=
456,225



Jacob wrote the equivalent equation below.



(
2
x
+
1
)
(
2
x
+
3
)
(
2
x
+
5
)
=
456,225



What does the left side of Jacob’s equation reveal about one of the clues the boys were given?




The three numbers are consecutive odd integers.


The three numbers are consecutive integers.


The three numbers are multiples of 2.


The three numbers are integers with last digits of 1, 3, and 5.

Answer 1

The three numbers are consecutive odd integers.

Reason: (2x+1), (2x+3), (2x+5) are integers that differ by 2, so they are consecutive odd integers.