Score:0/2 Penaltro 05 alf Question Watch Video If \( f(x)=x^{3}+3 x^{2}-33 x-35 \), which of the following is not a factor of \( f(x) \) ? Answer \( (x+7) \) \( (x-5) \) \( (x+1) \) \( (x+5) \)

We are given the function f(x) = x³ + 3x² - 33x - 35, and we need to determine which of the provided factors is not a factor of f(x). To check if a linear polynomial (x - a) (or equivalently (x + b), where b = -a) is a factor of f(x), we can use the Factor Theorem. The theorem states that (x - a) is a factor if and only if f(a) = 0. Let's test each candidate: 1. For (x + 7), set x = -7: f(-7) = (-7)³ + 3(-7)² - 33(-7) - 35 = -343 + 3(49) + 231 - 35 = -343 + 147 + 231 - 35 = 0. So, (x + 7) is a factor. 2. For (x - 5), set x = 5: f(5) = (5)³ + 3(5)² - 33(5) - 35 = 125 + 75 - 165 - 35 = 0. So, (x - 5) is a factor. 3. For (x + 1), set x = -1: f(-1) = (-1)³ + 3(-1)² - 33(-1) - 35 = -1 + 3 + 33 - 35 = 0. So, (x + 1) is a factor. 4. For (x + 5), set x = -5: f(-5) = (-5)³ + 3(-5)² - 33(-5) - 35 = -125 + 75 + 165 - 35 = 80 (not 0). So, (x + 5) is not a factor. Therefore, the factor that is not a factor of f(x) is (x + 5).