The question asks whether $x + 3$ is a factor of the polynomial $P(x) = x^3 - 7x^2 + 15x - 9$. To verify this, we use the Factor Theorem:

1. According to the Factor Theorem, $x + 3$ is a factor of $P(x)$ if and only if $P(-3) = 0$.
2. Substitute $x = -3$ into $P(x)$: $P(-3) = (-3)^3 - 7(-3)^2 + 15(-3) - 9$ Simplify step by step: $P(-3) = -27 - 7(9) + 15(-3) - 9$ $P(-3) = -27 - 63 - 45 - 9$ $P(-3) = -144$

Since $P(-3) \neq 0$, $x + 3$ is not a factor of $P(x)$.

Correct answer: B. False

Let me know if you want a detailed explanation of the Factor Theorem! Here are some related questions:

1. How do you verify if a different factor works for a polynomial?
2. Can synthetic division be used to test if $x + c$ is a factor? How?
3. What happens when $P(x)$ has repeated factors?
4. How does the Factor Theorem relate to the Remainder Theorem?
5. What are the possible ways to factorize a cubic polynomial like $x^3 - 7x^2 + 15x - 9$?

Tip: The Factor Theorem is a powerful tool for determining roots and simplifying polynomial division!