To find the values of 𝑥 that make the expression Which of the following is a value of x that makes the expression {(x²+5x+6)(x² - 7x+6)}(x² - 4x - 21) equal to zero Indicate all possible values of x.{(𝑥2+5𝑥+6)(𝑥2−7𝑥+6)}/(𝑥2−4𝑥−21) equal to zero, we need to find the values of 𝑥 that make the numerator equal to zero because division by zero is undefined.

First, let’s factor the numerator and denominator:

Numerator: (𝑥2+5𝑥+6)(𝑥2−7𝑥+6)

(𝑥2+5𝑥+6) factors as (𝑥+2)(𝑥+3).

(𝑥2−7𝑥+6) factors as (𝑥−1)(𝑥−6).

So, the numerator becomes (𝑥+2)(𝑥+3)(𝑥−1)(𝑥−6).

Denominator: 𝑥2−4𝑥−21

This quadratic expression factors as (𝑥−7)(𝑥+3).

So, the expression becomes:

{(𝑥+2)(𝑥+3)(𝑥−1)(𝑥−6)}/{(𝑥−7)(𝑥+3)}

To make the expression equal to zero, the numerator must be zero, while the denominator should not be zero. So, the values of 𝑥 that make the expression equal to zero are the values that make the numerator zero:

𝑥=−2,𝑥=−3,𝑥=1,𝑥=6

However, we need to exclude any values that would make the denominator zero, which are 𝑥=−3 and 𝑥=7. Therefore, the possible values of 𝑥 are:

𝑥=−2,𝑥=1,𝑥=6