Question

1. what is the product of three consecutive odd integers, if the one in the middle is ( x )?

( \bigcirc ) ( x^2 - 3x )
( \bigcirc ) ( x^2 - 5x )
( \bigcirc ) ( x^3 - x )
( \bigcirc ) ( x^3 - 4x )

Explanation:

Step1: Define the three integers

Let the three consecutive odd integers be $x-2$, $x$, $x+2$ (since consecutive odd integers differ by 2).

Step2: Compute their product

First multiply the first and third terms:
$$(x-2)(x+2) = x^2 - 4$$
Then multiply by the middle term $x$:
$$x(x^2 - 4) = x^3 - 4x$$

Answer:

$\boldsymbol{x^3 - 4x}$ (the fourth option)