Consider the polynomial p (x) = 8x^3-8x^2-2x+2.

Which binomial is not a factor of p (x) ?

2x+2

2x+1

2x-2

2x-1

Option A (2x+2).

Step-by-step 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!