Use the remainder theorem to find which of the following is NOT a factor of x^3 - 4x^2 - 4x + 16.

A.) x + 2

B.) x - 12

C.) x - 2

D.) x - 4

Answer: x - 12 is not a factor.

Step-by-step explanation:

The equation

x³ - 4x² - 4x + 16

To know which of the following is a factor, we continue to find the value of x and substitute into the equation and see the one that gives zero. The one that gives zero is the factor.

(a) x + 2

If x + 2 = 0

x = - 2, now substitute for x in the equation and find out if it will be zero.

x³ - 4x² - 4x + 16 = (-2) ³ - 4 (-2) ² - 4 (-2) + 16.

= - 8 - 16 + 8 + 16

= 0.

Therefore, x + 2 is a factor.

(b) x - 12

If x - 12 = 0, then x = 12

x³ - 4x² - 4x + 16

(12) ³ - 4 (12) ² - 4 (12) + 16

1728 - 576 - 48 + 16

= 1,120, not a factor.

(c) x - 2

If x - 2 = 0, then x = 2

x³ - 4x² - 4x + 16

(2) ³ - 4 (2) ² - 4 (2) + 16

8 - 16 - 8 + 16

= 0, Therefore, x - 2 is a factor.

(d) x - 4

If x - 4 = 0, x = 4

x³ - 4x² - 4x + 16

(4) ³ - 4 (4) ² - 4 (4) + 16

48 - 48 - 16 + 16

= 0, therefore, x - 4 is also a factor.