# Divide (10x^2-13x+12)÷(5x-1)

(10×2-13x+12)÷(5x-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 10×2 – 13x + 12
Divide the highest order term in the dividend 10×2 by the highest order term in divisor 5x.
 2x 5x – 1 10×2 – 13x + 12
Multiply the new quotient term by the divisor.
 2x 5x – 1 10×2 – 13x + 12 + 10×2 – 2x
The expression needs to be subtracted from the dividend, so change all the signs in 10×2-2x
 2x 5x – 1 10×2 – 13x + 12 – 10×2 + 2x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 2x 5x – 1 10×2 – 13x + 12 – 10×2 + 2x – 11x
Pull the next terms from the original dividend down into the current dividend.
 2x 5x – 1 10×2 – 13x + 12 – 10×2 + 2x – 11x + 12
Divide the highest order term in the dividend -11x by the highest order term in divisor 5x.
 2x – 115 5x – 1 10×2 – 13x + 12 – 10×2 + 2x – 11x + 12
Multiply the new quotient term by the divisor.
 2x – 115 5x – 1 10×2 – 13x + 12 – 10×2 + 2x – 11x + 12 – 11x + 115
The expression needs to be subtracted from the dividend, so change all the signs in -11x+115
 2x – 115 5x – 1 10×2 – 13x + 12 – 10×2 + 2x – 11x + 12 + 11x – 115
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 2x – 115 5x – 1 10×2 – 13x + 12 – 10×2 + 2x – 11x + 12 + 11x – 115 + 495
The final answer is the quotient plus the remainder over the divisor.
2x-115+495(5x-1)
Divide (10x^2-13x+12)÷(5x-1)