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!!!

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step-by-step explanation:

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step-by-step explanation:

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