# Divide (7x^3-8x^2-13x+2)÷(7x-1)

(7×3-8×2-13x+2)÷(7x-1)
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
 7x – 1 7×3 – 8×2 – 13x + 2
Divide the highest order term in the dividend 7×3 by the highest order term in divisor 7x.
 x2 7x – 1 7×3 – 8×2 – 13x + 2
Multiply the new quotient term by the divisor.
 x2 7x – 1 7×3 – 8×2 – 13x + 2 + 7×3 – x2
The expression needs to be subtracted from the dividend, so change all the signs in 7×3-x2
 x2 7x – 1 7×3 – 8×2 – 13x + 2 – 7×3 + x2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 x2 7x – 1 7×3 – 8×2 – 13x + 2 – 7×3 + x2 – 7×2
Pull the next terms from the original dividend down into the current dividend.
 x2 7x – 1 7×3 – 8×2 – 13x + 2 – 7×3 + x2 – 7×2 – 13x
Divide the highest order term in the dividend -7×2 by the highest order term in divisor 7x.
 x2 – x 7x – 1 7×3 – 8×2 – 13x + 2 – 7×3 + x2 – 7×2 – 13x
Multiply the new quotient term by the divisor.
 x2 – x 7x – 1 7×3 – 8×2 – 13x + 2 – 7×3 + x2 – 7×2 – 13x – 7×2 + x
The expression needs to be subtracted from the dividend, so change all the signs in -7×2+x
 x2 – x 7x – 1 7×3 – 8×2 – 13x + 2 – 7×3 + x2 – 7×2 – 13x + 7×2 – x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 x2 – x 7x – 1 7×3 – 8×2 – 13x + 2 – 7×3 + x2 – 7×2 – 13x + 7×2 – x – 14x
Pull the next terms from the original dividend down into the current dividend.
 x2 – x 7x – 1 7×3 – 8×2 – 13x + 2 – 7×3 + x2 – 7×2 – 13x + 7×2 – x – 14x + 2
Divide the highest order term in the dividend -14x by the highest order term in divisor 7x.
 x2 – x – 2 7x – 1 7×3 – 8×2 – 13x + 2 – 7×3 + x2 – 7×2 – 13x + 7×2 – x – 14x + 2
Multiply the new quotient term by the divisor.
 x2 – x – 2 7x – 1 7×3 – 8×2 – 13x + 2 – 7×3 + x2 – 7×2 – 13x + 7×2 – x – 14x + 2 – 14x + 2
The expression needs to be subtracted from the dividend, so change all the signs in -14x+2
 x2 – x – 2 7x – 1 7×3 – 8×2 – 13x + 2 – 7×3 + x2 – 7×2 – 13x + 7×2 – x – 14x + 2 + 14x – 2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 x2 – x – 2 7x – 1 7×3 – 8×2 – 13x + 2 – 7×3 + x2 – 7×2 – 13x + 7×2 – x – 14x + 2 + 14x – 2 0
Since the remander is 0, the final answer is the quotient.
x2-x-2
Divide (7x^3-8x^2-13x+2)÷(7x-1)