Divide (4k^3-30k^2-106k+64)÷(k-10)

Math
(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.
k104k330k2106k+64
Divide the highest order term in the dividend 4k3 by the highest order term in divisor k.
4k2
k104k330k2106k+64
Multiply the new quotient term by the divisor.
4k2
k104k330k2106k+64
+4k340k2
The expression needs to be subtracted from the dividend, so change all the signs in 4k3-40k2
4k2
k104k330k2106k+64
4k3+40k2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
4k2
k104k330k2106k+64
4k3+40k2
+10k2
Pull the next terms from the original dividend down into the current dividend.
4k2
k104k330k2106k+64
4k3+40k2
+10k2106k
Divide the highest order term in the dividend 10k2 by the highest order term in divisor k.
4k2+10k
k104k330k2106k+64
4k3+40k2
+10k2106k
Multiply the new quotient term by the divisor.
4k2+10k
k104k330k2106k+64
4k3+40k2
+10k2106k
+10k2100k
The expression needs to be subtracted from the dividend, so change all the signs in 10k2-100k
4k2+10k
k104k330k2106k+64
4k3+40k2
+10k2106k
10k2+100k
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
4k2+10k
k104k330k2106k+64
4k3+40k2
+10k2106k
10k2+100k
6k
Pull the next terms from the original dividend down into the current dividend.
4k2+10k
k104k330k2106k+64
4k3+40k2
+10k2106k
10k2+100k
6k+64
Divide the highest order term in the dividend -6k by the highest order term in divisor k.
4k2+10k6
k104k330k2106k+64
4k3+40k2
+10k2106k
10k2+100k
6k+64
Multiply the new quotient term by the divisor.
4k2+10k6
k104k330k2106k+64
4k3+40k2
+10k2106k
10k2+100k
6k+64
6k+60
The expression needs to be subtracted from the dividend, so change all the signs in -6k+60
4k2+10k6
k104k330k2106k+64
4k3+40k2
+10k2106k
10k2+100k
6k+64
+6k60
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
4k2+10k6
k104k330k2106k+64
4k3+40k2
+10k2106k
10k2+100k
6k+64
+6k60
+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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