when f(x)=2x^3−11x^3−4x+a is divided by x+2, the remainder is −4. What is the value of a

Answer 1

By the Remainder Theorem, f(-2) = -4. So, evaluate f(x) at x = -2 and solve for a.

Or, do a synthetic division and see what the remainder is. Set that equal to -4 and solve for a.

Answer 2

i get -56 but how do i know this is right, when i plug -2 into equation i get 24

Answer 3

As it is written,

f(-2) = 80+a
So, 80+a = -4
means a = -84

But, there is apparently a typo in f(x). If we set

f(x) = 2x^3−11x^2−4x+a
f(-2) = -52+a = -4
so, a = 48

So, how did you come by your results? I showed you mine. Show me yours.

Answer 4

i did synthetic division and got to 52 and since the remainder is -4 i made a= -56
the multiple choice answers are
a)48
b)56
c)48
d)-56

Answer 5

When you do the synthetic division, there will be an "a" in the remainder. The remainder is -52+a

So, you set -52+a = -4 and get a=48

The bottom row of the division is

2 -15 26 -52+a