Question

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

Answer 1

C) -123

Explanation:

x + 4 = 0

x = -4

3(-4)³ − (-4)2 − 20(-4) + 5

-123

Answer 2

-123

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