# Divide (p^3-6)/(p-1) 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.
 p – 1 p3 + 0p2 + 0p – 6
Divide the highest order term in the dividend p3 by the highest order term in divisor p.
 p2 p – 1 p3 + 0p2 + 0p – 6
Multiply the new quotient term by the divisor.
 p2 p – 1 p3 + 0p2 + 0p – 6 + p3 – p2
The expression needs to be subtracted from the dividend, so change all the signs in p3-p2
 p2 p – 1 p3 + 0p2 + 0p – 6 – p3 + p2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 p2 p – 1 p3 + 0p2 + 0p – 6 – p3 + p2 + p2
Pull the next terms from the original dividend down into the current dividend.
 p2 p – 1 p3 + 0p2 + 0p – 6 – p3 + p2 + p2 + 0p
Divide the highest order term in the dividend p2 by the highest order term in divisor p.
 p2 + p p – 1 p3 + 0p2 + 0p – 6 – p3 + p2 + p2 + 0p
Multiply the new quotient term by the divisor.
 p2 + p p – 1 p3 + 0p2 + 0p – 6 – p3 + p2 + p2 + 0p + p2 – p
The expression needs to be subtracted from the dividend, so change all the signs in p2-p
 p2 + p p – 1 p3 + 0p2 + 0p – 6 – 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 p – 1 p3 + 0p2 + 0p – 6 – p3 + p2 + p2 + 0p – p2 + p + p
Pull the next terms from the original dividend down into the current dividend.
 p2 + p p – 1 p3 + 0p2 + 0p – 6 – p3 + p2 + p2 + 0p – p2 + p + p – 6
Divide the highest order term in the dividend p by the highest order term in divisor p.
 p2 + p + 1 p – 1 p3 + 0p2 + 0p – 6 – p3 + p2 + p2 + 0p – p2 + p + p – 6
Multiply the new quotient term by the divisor.
 p2 + p + 1 p – 1 p3 + 0p2 + 0p – 6 – p3 + p2 + p2 + 0p – p2 + p + p – 6 + p – 1
The expression needs to be subtracted from the dividend, so change all the signs in p-1
 p2 + p + 1 p – 1 p3 + 0p2 + 0p – 6 – p3 + p2 + p2 + 0p – p2 + p + p – 6 – p + 1
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 p2 + p + 1 p – 1 p3 + 0p2 + 0p – 6 – p3 + p2 + p2 + 0p – p2 + p + p – 6 – p + 1 – 5
The final answer is the quotient plus the remainder over the divisor.
p2+p+1-5p-1
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