# Divide (z^4z^6)/(z^5z-3)

z4z6z5z-3
Expand z4z6.
Use the power rule aman=am+n to combine exponents.
z4+6z5z-3
z10z5z-3
z10z5z-3
Expand z5z-3.
Use the power rule aman=am+n to combine exponents.
z10z5+1-3
z10z6-3
z10z6-3
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
 z6 + 0z5 + 0z4 + 0z3 + 0z2 + 0z – 3 z10 + 0z9 + 0z8 + 0z7 + 0z6 + 0z5 + 0z4 + 0z3 + 0z2 + 0z + 0
Divide the highest order term in the dividend z10 by the highest order term in divisor z6.
 z4 z6 + 0z5 + 0z4 + 0z3 + 0z2 + 0z – 3 z10 + 0z9 + 0z8 + 0z7 + 0z6 + 0z5 + 0z4 + 0z3 + 0z2 + 0z + 0
Multiply the new quotient term by the divisor.
 z4 z6 + 0z5 + 0z4 + 0z3 + 0z2 + 0z – 3 z10 + 0z9 + 0z8 + 0z7 + 0z6 + 0z5 + 0z4 + 0z3 + 0z2 + 0z + 0 + z10 + 0 + 0 + 0 + 0 + 0 – 3z4
The expression needs to be subtracted from the dividend, so change all the signs in z10+0+0+0+0+0-3z4
 z4 z6 + 0z5 + 0z4 + 0z3 + 0z2 + 0z – 3 z10 + 0z9 + 0z8 + 0z7 + 0z6 + 0z5 + 0z4 + 0z3 + 0z2 + 0z + 0 – z10 – 0 – 0 – 0 – 0 – 0 + 3z4
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 z4 z6 + 0z5 + 0z4 + 0z3 + 0z2 + 0z – 3 z10 + 0z9 + 0z8 + 0z7 + 0z6 + 0z5 + 0z4 + 0z3 + 0z2 + 0z + 0 – z10 – 0 – 0 – 0 – 0 – 0 + 3z4 + 3z4
Pull the next terms from the original dividend down into the current dividend.
 z4 z6 + 0z5 + 0z4 + 0z3 + 0z2 + 0z – 3 z10 + 0z9 + 0z8 + 0z7 + 0z6 + 0z5 + 0z4 + 0z3 + 0z2 + 0z + 0 – z10 – 0 – 0 – 0 – 0 – 0 + 3z4 + 3z4 + 0z3 + 0z2 + 0z + 0
The final answer is the quotient plus the remainder over the divisor.
z4+3z4z6-3
Divide (z^4z^6)/(z^5z-3)