Divide (p^3-6)/(p-1)

Math
p3-6p-1
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
p1p3+0p2+0p6
Divide the highest order term in the dividend p3 by the highest order term in divisor p.
p2
p1p3+0p2+0p6
Multiply the new quotient term by the divisor.
p2
p1p3+0p2+0p6
+p3p2
The expression needs to be subtracted from the dividend, so change all the signs in p3-p2
p2
p1p3+0p2+0p6
p3+p2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
p2
p1p3+0p2+0p6
p3+p2
+p2
Pull the next terms from the original dividend down into the current dividend.
p2
p1p3+0p2+0p6
p3+p2
+p2+0p
Divide the highest order term in the dividend p2 by the highest order term in divisor p.
p2+p
p1p3+0p2+0p6
p3+p2
+p2+0p
Multiply the new quotient term by the divisor.
p2+p
p1p3+0p2+0p6
p3+p2
+p2+0p
+p2p
The expression needs to be subtracted from the dividend, so change all the signs in p2-p
p2+p
p1p3+0p2+0p6
p3+p2
+p2+0p
p2+p
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
p2+p
p1p3+0p2+0p6
p3+p2
+p2+0p
p2+p
+p
Pull the next terms from the original dividend down into the current dividend.
p2+p
p1p3+0p2+0p6
p3+p2
+p2+0p
p2+p
+p6
Divide the highest order term in the dividend p by the highest order term in divisor p.
p2+p+1
p1p3+0p2+0p6
p3+p2
+p2+0p
p2+p
+p6
Multiply the new quotient term by the divisor.
p2+p+1
p1p3+0p2+0p6
p3+p2
+p2+0p
p2+p
+p6
+p1
The expression needs to be subtracted from the dividend, so change all the signs in p-1
p2+p+1
p1p3+0p2+0p6
p3+p2
+p2+0p
p2+p
+p6
p+1
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
p2+p+1
p1p3+0p2+0p6
p3+p2
+p2+0p
p2+p
+p6
p+1
5
The final answer is the quotient plus the remainder over the divisor.
p2+p+1-5p-1
Divide (p^3-6)/(p-1)

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