Solve the polynomial equation p(x)=x^3+2x^2-5x-6. Which of the following is a factor? (1 point) x+1 x-3 x+2 x-1

To determine which of the options is a factor of the polynomial \( p(x) = x^3 + 2x^2 - 5x - 6 \), we can use the Factor Theorem. According to the Factor Theorem, \( x - c \) is a factor of \( p(x) \) if and only if \( p(c) = 0 \).

Let's evaluate \( p(x) \) at each of the potential roots from the options:

1. Testing \( x = -1 \): \[ p(-1) = (-1)^3 + 2(-1)^2 - 5(-1) - 6 = -1 + 2 + 5 - 6 = 0 \]

   Since \( p(-1) = 0 \), \( x + 1 \) is a factor of the polynomial.

2. Testing \( x = 3 \): \[ p(3) = (3)^3 + 2(3)^2 - 5(3) - 6 = 27 + 18 - 15 - 6 = 24 \neq 0 \]

3. Testing \( x = -2 \): \[ p(-2) = (-2)^3 + 2(-2)^2 - 5(-2) - 6 = -8 + 8 + 10 - 6 = 4 \neq 0 \]

4. Testing \( x = 1 \): \[ p(1) = (1)^3 + 2(1)^2 - 5(1) - 6 = 1 + 2 - 5 - 6 = -8 \neq 0 \]

From our evaluations, we find that \( x + 1 \) is indeed a factor of the polynomial \( p(x) = x^3 + 2x^2 - 5x - 6 \).

Therefore, the correct answer is \( x + 1 \).