Calculate the quotient and remainder of (x^{3}+2x^{2}-4x+3) ÷ (x^{2}-1)

Start by rewriting the problem in long division notation.
Make sure there are no missing exponents in either the divisor or dividend. In this problem the divisor has no x term; you should write it with a coefficient of 0.

Answer the question: "What times the first term in the divisor, x^{2} will give me exactly the first term in the dividen, x^{3}?" The answer is x, so you should write x above -4x, since it and the number you just came up with x are like terms.

Multiply the divisor by x and write the result below the dividend:

Now multiply everything in that bottom line by -1 and then combine the like terms.

Drop down the next term in the dividend polynomial, in this case +3 and repeat the process until there are no more terms to drop.

The quotient is the quantity above the division symbol, x+2 and the remainder is -3x+1