What is m if p=2x^4-mx^3+x^2-7 divided by x+2 to have the reminder r=4 ?

According to the fundamental theorem of algebra, if
P(x) is divided by (x+2) and the reminder is 4, then we could
write:

P(-2)=4 (1)

We'll
apply the rule of division with reminder:

2X^4 - mX^3 + X^2
- 7= Q(x+2) + 4

But P(-2)=4, so, we'll substitute x by -2
in the expression of polynomial P(x).

P(-2) = 2(-2)^4 -
m(-2)^3 + (-2)^2 - 7

P(-2) = 32 + 8m + 4 -
7

We'll substitute P(-2) by
4:

4 = 8m + 29

We'll use the
symmetric property:

8m + 29 =
4

We'll subtract 29:

8m = 4 -
29

8m = -25

We'll divide by
8:

m =
-25/8

The polynomial P(x),
whose reminder is 4 when it's divided by (x+2), is determined for m =
-25/8.