# Divide (4k^3-30k^2-106k+64)÷(k-10)

(4k3-30k2-106k+64)÷(k-10)
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
 k – 10 4k3 – 30k2 – 106k + 64
Divide the highest order term in the dividend 4k3 by the highest order term in divisor k.
 4k2 k – 10 4k3 – 30k2 – 106k + 64
Multiply the new quotient term by the divisor.
 4k2 k – 10 4k3 – 30k2 – 106k + 64 + 4k3 – 40k2
The expression needs to be subtracted from the dividend, so change all the signs in 4k3-40k2
 4k2 k – 10 4k3 – 30k2 – 106k + 64 – 4k3 + 40k2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 4k2 k – 10 4k3 – 30k2 – 106k + 64 – 4k3 + 40k2 + 10k2
Pull the next terms from the original dividend down into the current dividend.
 4k2 k – 10 4k3 – 30k2 – 106k + 64 – 4k3 + 40k2 + 10k2 – 106k
Divide the highest order term in the dividend 10k2 by the highest order term in divisor k.
 4k2 + 10k k – 10 4k3 – 30k2 – 106k + 64 – 4k3 + 40k2 + 10k2 – 106k
Multiply the new quotient term by the divisor.
 4k2 + 10k k – 10 4k3 – 30k2 – 106k + 64 – 4k3 + 40k2 + 10k2 – 106k + 10k2 – 100k
The expression needs to be subtracted from the dividend, so change all the signs in 10k2-100k
 4k2 + 10k k – 10 4k3 – 30k2 – 106k + 64 – 4k3 + 40k2 + 10k2 – 106k – 10k2 + 100k
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 4k2 + 10k k – 10 4k3 – 30k2 – 106k + 64 – 4k3 + 40k2 + 10k2 – 106k – 10k2 + 100k – 6k
Pull the next terms from the original dividend down into the current dividend.
 4k2 + 10k k – 10 4k3 – 30k2 – 106k + 64 – 4k3 + 40k2 + 10k2 – 106k – 10k2 + 100k – 6k + 64
Divide the highest order term in the dividend -6k by the highest order term in divisor k.
 4k2 + 10k – 6 k – 10 4k3 – 30k2 – 106k + 64 – 4k3 + 40k2 + 10k2 – 106k – 10k2 + 100k – 6k + 64
Multiply the new quotient term by the divisor.
 4k2 + 10k – 6 k – 10 4k3 – 30k2 – 106k + 64 – 4k3 + 40k2 + 10k2 – 106k – 10k2 + 100k – 6k + 64 – 6k + 60
The expression needs to be subtracted from the dividend, so change all the signs in -6k+60
 4k2 + 10k – 6 k – 10 4k3 – 30k2 – 106k + 64 – 4k3 + 40k2 + 10k2 – 106k – 10k2 + 100k – 6k + 64 + 6k – 60
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 4k2 + 10k – 6 k – 10 4k3 – 30k2 – 106k + 64 – 4k3 + 40k2 + 10k2 – 106k – 10k2 + 100k – 6k + 64 + 6k – 60 + 4
The final answer is the quotient plus the remainder over the divisor.
4k2+10k-6+4k-10
Divide (4k^3-30k^2-106k+64)÷(k-10)

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