Answer:
Option A (2x+2).
Explanation:
p(x) = 8x^3 - 8x^2 - 2x + 2.
This question will be solved using the factor theorem. First, all the binomials have to be equated to 0 and presented in the form x = c, where c is a real number. Therefore:
1) 2x+2 = 0. This implies x = -1.
2) 2x+1 = 0. This implies x = -1/2.
3) 2x-2 = 0. This implies x = 1.
4) 2x-1= 0. This implies x = 1/2.
Now we have the values which have to be substituted in p(x). In order to be a factor, any number c should satisfy the following condition: p(c) = 0. Now checking for each option:
1) p(-1) = 8(-1)^3 - 8(-1)^2 - 2(-1) + 2 = - 8 - 8 + 2 + 2 = -12.
2) p(-1/2) = 8(-1/2)^3 - 8(-1/2)^2 - 2(-1/2) + 2 = - 1 - 2 + 1 + 2 = 0.
3) p(1) = 8(1)^3 - 8(1)^2 - 2(1) + 2 = 8 - 8 - 2 + 2 = 0.
4) p(1/2) = 8(1/2)^3 - 8(1/2)^2 - 2(1/2) + 2 = 1 - 2 - 1 + 2 = 0.
It can be seen that p(-1) is not equal to 0. This means that 2x+2 is not the factor of p(x). So according to the factor theorem, Option A is the correct answer!!!