Long division of a polynomial

Question

I am having a very hard time dividing this polynomial, can someone help? I think it is because the dividend is squared;

 

3x^4 + x^3 - 2x^2 + 3x - 4 divided by x^2 - 1

 

 

I choke on the x^3 point

Answer 1

This window does not allow for easy long division format, so I will try to give a line by line version.

First x² divides into 3x⁴ giving 3x² as the first term in your answer.

Multiplying 3x² by the divisor gives 3x⁴ - 3x². 

By subtraction this leaves x³ + x² + 3x - 4.

Dividing again by x² gives x as the second term in your answer.

Multiplying x by the divisor gives x³ - x.

By subtraction this leaves x² + 4x - 4.

Dividing again by x² gives 1 as the third term in your answer.

Multiplying 1 by the divisor gives x² - 1.

By subtraction this leaves 4x - 3 as the remainder.

The answer is 3x² + x + 1 with remainder 4x - 3.

I hope this helps!

Answer 2

Ray,

        If you write x²-1 as x²+0x-1 and cary out the division as with the 0x as a placeholder you will get it

 

The typing is very messy the answer I got is  3x²+x+1 +(4x-3)/(x²-1)

 

Hope this helps

 

Jim