Question

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

Answer 1

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.