Find the remainder of (x^4 – 2) ÷ (x + 1).?

(ax^3 + bx^2 + cx + d + e/(x + 1)) * (x + 1) = x^4 - 2

ax^3 * (x + 1) + bx^2 * (x + 1) + cx * (x + 1) + d * (x + 1) + e * (x + 1) / (x + 1) = x^4 + 0x^3 + 0x^2 + 0x - 2
ax^4 + ax^3 + bx^3 + bx^2 + cx^2 + cx + dx + d + e = x^4 + 0x^3 + 0x^2 + 0x - 2

ax^4 = x^4
a = 1

ax^3 + bx^3 = 0x^3
a + b = 0
1 + b = 0
b = -1

bx^2 + cx^2 = 0x^2
-1 + c = 0
c = 1

cx + dx = 0x
1 + d = 0
d = -1

d + e = -2
-1 + e = -2
e = -1

The remainder will be -1

Let f(x) = x⁴ - 2

By remainder theorem, the remainder of (x⁴ – 2) ÷ (x + 1)
= f(-1)
= (-1)⁴ - 2
= -1

Let p (x) = x^4 -1
By remainder theorem remainder on division on p (x) by (x-a) is p (a)
Therefore remainder =p (-1) = (-1)^4 -2 = -1