Question

Which of the following is a product of 3 consecutive integers? show your work.

A) 8
B) 7
C) 2
D) 1
E) 0

Answer 1

The answer is B it’s 7 bcuz it’s 7

Answer 2

E) 0

Explanation:

You want to identify the value on the given list that is the product of three consecutive integers.

Product

If we let n represent the middle of the three integers, then we have ...

product = (n -1)(n)(n +1) = n(n² -1)

Parity

We can see that when n is even, the product will be (even)×(odd) = even.

When n is odd, the product will be (odd)×(even) = even.

This eliminates choices B and D.

The zero product rule tells us that the product will be 0 if n=0, which is to say that the product of the consecutive integers -1, 0, 1 will be 0.

The product must have three consecutive integer factors, so cannot be 2 or 8. This eliminates choices A and C.

8 = 1·2·4 . . . non-consecutive integers

2 = 1·1·2 . . . non-consecutive integers