Divide using long division: x^3+4x^2-x-2/x+2?

Question

Algebra division of Polynomials. Need Help Please.

Answer 1

.........x^2+2x-5
x+2 ) x^3 + 4x^2 - x - 2
.........x^3 + 2x^2
........----------------
...................2x^2 - x
...................2x^2 + 4x
...................-------------
....................-5x - 2
....................-5x-10
......................---------
...........................8

x^2 + 2x -5+8/(x+2)

Answer 2

x^3 + 4x^2 - x - 2 ( x + 2 (Ans: x^2 + 2x - 5
x^3 +2x^2 (Subtract)
________
0x^3 + 2x^2 - x
0x^3 + 2x^2 +4x (Subtract)
_______________
0x^3 + 0x^2 - 5x - 2
ox^3 + 0x^2 -5x + 10 (Subtract)
_________________
0x^3 +0x^2 + 0x - 12

So answer is :- x^2 + 2x -5 Remainder -12

Abother way is :-

x^3 + 4x^2 - x - 2 = (x+2)(ax^2 + bx + c) + d
= ax^3 +bx^2 +cx +2ax^2 + 2bx + 2c + d
= ax^3 +(2a + b)x^2 + (2b + c)x + 2c + d
Equating coefficients x^3 gives a = 1

Equating coefficients of x^2 gives (2a + b) = 4
2(1) + b = 4
b = 2
Equating coefficients of x gives (2b + c) = -1
2(2) + c = -1
c = -5
Equating constants 2c + d = 2
2(-5) + d = 2
d = 12 the remainder

Hence x + 2 is NOT a factor of x^3 + 4x^2 - x - 2