# Divide (-10x+25x^2-8)/(5x-1)

-10x+25×2-85x-1
Reorder -10x and 25×2.
25×2-10x-85x-1
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
 5x – 1 25×2 – 10x – 8
Divide the highest order term in the dividend 25×2 by the highest order term in divisor 5x.
 5x 5x – 1 25×2 – 10x – 8
Multiply the new quotient term by the divisor.
 5x 5x – 1 25×2 – 10x – 8 + 25×2 – 5x
The expression needs to be subtracted from the dividend, so change all the signs in 25×2-5x
 5x 5x – 1 25×2 – 10x – 8 – 25×2 + 5x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 5x 5x – 1 25×2 – 10x – 8 – 25×2 + 5x – 5x
Pull the next terms from the original dividend down into the current dividend.
 5x 5x – 1 25×2 – 10x – 8 – 25×2 + 5x – 5x – 8
Divide the highest order term in the dividend -5x by the highest order term in divisor 5x.
 5x – 1 5x – 1 25×2 – 10x – 8 – 25×2 + 5x – 5x – 8
Multiply the new quotient term by the divisor.
 5x – 1 5x – 1 25×2 – 10x – 8 – 25×2 + 5x – 5x – 8 – 5x + 1
The expression needs to be subtracted from the dividend, so change all the signs in -5x+1
 5x – 1 5x – 1 25×2 – 10x – 8 – 25×2 + 5x – 5x – 8 + 5x – 1
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 5x – 1 5x – 1 25×2 – 10x – 8 – 25×2 + 5x – 5x – 8 + 5x – 1 – 9
The final answer is the quotient plus the remainder over the divisor.
5x-1-95x-1
Divide (-10x+25x^2-8)/(5x-1)