Step-by-step explanation:
We can use the following theorem:
Theorem: If (x + a) is a factor of P(x), then P(-a) = 0.
In other words, if we substitute -a for x in P(x), and we get 0, then (x + a) is a factor of P(x).
In this case, we have P(x) = x³ + 3x² - 6x - 7. Substituting -1 for x, we get:
P(-1) = (-1)³ + 3(-1)² - 6(-1) - 7 = -1 + 3 + 6 - 7 = 0
Therefore, (x + 1) is a factor of P(x)
