Thread: Abstract Algebra

I really need some help getting started with this polynomial division problem. I need to find the gcd of x+a+b and x^3-3abx+a^3+b^3.

Thanks

Here's a link to dividing long polynomials: Polynomial Long Division

Think of the problem as:

You will see that you'll get a remainder of 0, indicating that:

Ok, so the first term in the quotient is x^2. I just do not know where to go with that. Do you get x^3+(a+b)x^2 and how do you subtract that from x^3+0x^2. How do you ever get the a+b without the x so you can subtract the a^3+b^3 terms? I just do not see how you get this done.

Thanks,

When dividing, we always match the leftmost term of each line so that when subtracting, they disappear (those in colour):



LaTex is kind of hard to work with when it comes to long division but hopefully, you can see where to go from here. Treat all the terms with s and s as constants in front of .

Ok,
I think it finally clicked.

Thank you very much.