MathMaster

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

Math
z4z6z5z-3
Expand z4z6.
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Use the power rule aman=am+n to combine exponents.
z4+6z5z-3
Add 4 and 6.
z10z5z-3
z10z5z-3
Expand z5z-3.
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Use the power rule aman=am+n to combine exponents.
z10z5+1-3
Add 5 and 1.
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–3z10+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–3z10+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–3z10+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–3z10+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–3z10+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–3z10+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)

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