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3x2 - 2 is a polynomial of order 2.
Therefore, dividing it by (x + 1) will result in a polynomial of order 1. Suppose the quotient is ax + b (where a is non-zero), and with the remainder c.
Thus 3x2 - 2 = (x + 1)*(ax + b) + c
= ax2 + ax + bx + b + c
= ax2 + (a + b)x + (b + c)
Comparing coefficients:
3 = a
0 = a + b => 0 = 3 + b => b = -3
-2 = b + c => -2 = -3 + c => c = 1
Therefore, (3x2 - 2)/(x + 1) = 3x - 3 = 3*(x - 1) and a remainder of 1.
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