By using the remainder theorem, determine the remainder when

3x^3 - x^2 - 20x + 5 is divided by (x + 4)

Select the appropriate response:

A) - 140

B) 175

C) - 123

D) 123

C) - 123

Step-by-step explanation:

x + 4 = 0

x = - 4

3 (-4) ³ - (-4) 2 - 20 (-4) + 5

-123

-123

Step-by-step explanation:

The remainder theorem says that when a polynomial is divided by a linear factor x - c (note the minus sign), the remainder is the value of the polynomial at x = c.

When a polynomial P (x) is divided by x - c, the remainder is P (c). In other words, to find the remainder, plug in c for x.

You're dividing by x + 4 which is the same thing as x - (-4) - - the role of c is being played by - 4.

3 (-4) ^3 - (-4) ^2 - 20 (-4) + 5 = - 123