1. **Problem:** Examine whether $x - 1$ is a factor of the polynomial $4x^3 + 3x^2 - 4x - 3$. 2. **Rule:** To check if $x - 1$ is a factor, use the Factor Theorem which states that if $x - a$ is a factor of a polynomial $f(x)$, then $f(a) = 0$. 3. **Apply:** Here, $a = 1$. Evaluate $f(1) = 4(1)^3 + 3(1)^2 - 4(1) - 3 = 4 + 3 - 4 - 3 = 0$. 4. Since $f(1) = 0$, $x - 1$ is a factor of $4x^3 + 3x^2 - 4x - 3$. --- 1. **Problem:** Examine whether $x - 1$ is a factor of the polynomial $x^3 - 3x^2 - 9x + 5$. 2. **Apply Factor Theorem:** Evaluate $f(1) = 1^3 - 3(1)^2 - 9(1) + 5 = 1 - 3 - 9 + 5 = -6$. 3. Since $f(1) \neq 0$, $x - 1$ is not a factor of $x^3 - 3x^2 - 9x + 5$. --- **Final answers:** - $x - 1$ is a factor of $4x^3 + 3x^2 - 4x - 3$. - $x - 1$ is not a factor of $x^3 - 3x^2 - 9x + 5$.