The dividend and divisor are sorted in descending order related to x.
Divide the first term of the dividend by the first divider of x.
This is the first term of the quotient.
Multiplied this term by each of the terms of the divisor and as these products have to subtract from dividing.
These products with their signs changed the writing under the similar terms with them and make the dividend reduction.
The second term of the quotient. This must be multiplied by each of the terms of the divisor and subtract the product of the dividend.
We write these terms below their similar and by the reduction gives zero residue.
I do hope you can find it useful.