**Explanation:**

To determine if (x + 3) is a factor of the polynomial x^3 + x^2 + 4x + 6, we can use the Factor Theorem. According to the Factor Theorem, if a polynomial P(x) is divided by (x - a), then the remainder is zero if and only if P(a) = 0.

In this case, we need to determine if P(-3) = 0 for the given polynomial P(x) = x^3 + x^2 + 4x + 6.

**Step 1: Evaluate P(-3)**

Substituting -3 for x in the polynomial P(x), we get:

P(-3) = (-3)^3 + (-3)^2 + 4(-3) + 6
= -27 + 9 - 12 + 6
= -24

Therefore, P(-3) is equal to -24.

**Step 2: Analyze the result**

Since P(-3) is not equal to zero, we can conclude that (x + 3) is not a factor of the polynomial x^3 + x^2 + 4x + 6.

If (x + 3) were a factor, then P(-3) would be equal to zero. However, since P(-3) is not zero, (x + 3) is not a factor.

Hence, (x + 3) is not a factor of x^3 + x^2 + 4x + 6.

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