Which of the following is a factor of  2x3−x2−13x−62𝑥3−𝑥2−13𝑥−6.Select one:A.(x−1)(𝑥−1)B.(x+1)(𝑥+1)C.(x−2)(𝑥−2)D.(x+2)

To find out which of the options is a factor of the given polynomial, we can use the Factor Theorem which states that a polynomial f(x) has a factor (x - k) if and only if f(k) = 0.

Let's test each option:

A. (x - 1) Substitute x = 1 into the polynomial: 2(1)^3 - (1)^2 - 13(1) - 6 = 2 - 1 - 13 - 6 = -18 ≠ 0 So, (x - 1) is not a factor.

B. (x + 1) Substitute x = -1 into the polynomial: 2(-1)^3 - (-1)^2 - 13(-1) - 6 = -2 - 1 + 13 - 6 = 4 ≠ 0 So, (x + 1) is not a factor.

C. (x - 2) Substitute x = 2 into the polynomial: 2(2)^3 - (2)^2 - 13(2) - 6 = 16 - 4 - 26 - 6 = -20 ≠ 0 So, (x - 2) is not a factor.

D. (x + 2) Substitute x = -2 into the polynomial: 2(-2)^3 - (-2)^2 - 13(-2) - 6 = -16 - 4 + 26 - 6 = 0 So, (x + 2) is a factor.

Therefore, the correct answer is D. (x + 2).