# Divide (5x^3-26x^2-29x+30)/(x-6)

5×3-26×2-29x+30x-6
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
 x – 6 5×3 – 26×2 – 29x + 30
Divide the highest order term in the dividend 5×3 by the highest order term in divisor x.
 5×2 x – 6 5×3 – 26×2 – 29x + 30
Multiply the new quotient term by the divisor.
 5×2 x – 6 5×3 – 26×2 – 29x + 30 + 5×3 – 30×2
The expression needs to be subtracted from the dividend, so change all the signs in 5×3-30×2
 5×2 x – 6 5×3 – 26×2 – 29x + 30 – 5×3 + 30×2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 5×2 x – 6 5×3 – 26×2 – 29x + 30 – 5×3 + 30×2 + 4×2
Pull the next terms from the original dividend down into the current dividend.
 5×2 x – 6 5×3 – 26×2 – 29x + 30 – 5×3 + 30×2 + 4×2 – 29x
Divide the highest order term in the dividend 4×2 by the highest order term in divisor x.
 5×2 + 4x x – 6 5×3 – 26×2 – 29x + 30 – 5×3 + 30×2 + 4×2 – 29x
Multiply the new quotient term by the divisor.
 5×2 + 4x x – 6 5×3 – 26×2 – 29x + 30 – 5×3 + 30×2 + 4×2 – 29x + 4×2 – 24x
The expression needs to be subtracted from the dividend, so change all the signs in 4×2-24x
 5×2 + 4x x – 6 5×3 – 26×2 – 29x + 30 – 5×3 + 30×2 + 4×2 – 29x – 4×2 + 24x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 5×2 + 4x x – 6 5×3 – 26×2 – 29x + 30 – 5×3 + 30×2 + 4×2 – 29x – 4×2 + 24x – 5x
Pull the next terms from the original dividend down into the current dividend.
 5×2 + 4x x – 6 5×3 – 26×2 – 29x + 30 – 5×3 + 30×2 + 4×2 – 29x – 4×2 + 24x – 5x + 30
Divide the highest order term in the dividend -5x by the highest order term in divisor x.
 5×2 + 4x – 5 x – 6 5×3 – 26×2 – 29x + 30 – 5×3 + 30×2 + 4×2 – 29x – 4×2 + 24x – 5x + 30
Multiply the new quotient term by the divisor.
 5×2 + 4x – 5 x – 6 5×3 – 26×2 – 29x + 30 – 5×3 + 30×2 + 4×2 – 29x – 4×2 + 24x – 5x + 30 – 5x + 30
The expression needs to be subtracted from the dividend, so change all the signs in -5x+30
 5×2 + 4x – 5 x – 6 5×3 – 26×2 – 29x + 30 – 5×3 + 30×2 + 4×2 – 29x – 4×2 + 24x – 5x + 30 + 5x – 30
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 5×2 + 4x – 5 x – 6 5×3 – 26×2 – 29x + 30 – 5×3 + 30×2 + 4×2 – 29x – 4×2 + 24x – 5x + 30 + 5x – 30 0
Since the remander is 0, the final answer is the quotient.
5×2+4x-5
Divide (5x^3-26x^2-29x+30)/(x-6)

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