# Divide (4x^3-6x^2-8x+1)/(2x-4)

4×3-6×2-8x+12x-4
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
 2x – 4 4×3 – 6×2 – 8x + 1
Divide the highest order term in the dividend 4×3 by the highest order term in divisor 2x.
 2×2 2x – 4 4×3 – 6×2 – 8x + 1
Multiply the new quotient term by the divisor.
 2×2 2x – 4 4×3 – 6×2 – 8x + 1 + 4×3 – 8×2
The expression needs to be subtracted from the dividend, so change all the signs in 4×3-8×2
 2×2 2x – 4 4×3 – 6×2 – 8x + 1 – 4×3 + 8×2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 2×2 2x – 4 4×3 – 6×2 – 8x + 1 – 4×3 + 8×2 + 2×2
Pull the next terms from the original dividend down into the current dividend.
 2×2 2x – 4 4×3 – 6×2 – 8x + 1 – 4×3 + 8×2 + 2×2 – 8x
Divide the highest order term in the dividend 2×2 by the highest order term in divisor 2x.
 2×2 + x 2x – 4 4×3 – 6×2 – 8x + 1 – 4×3 + 8×2 + 2×2 – 8x
Multiply the new quotient term by the divisor.
 2×2 + x 2x – 4 4×3 – 6×2 – 8x + 1 – 4×3 + 8×2 + 2×2 – 8x + 2×2 – 4x
The expression needs to be subtracted from the dividend, so change all the signs in 2×2-4x
 2×2 + x 2x – 4 4×3 – 6×2 – 8x + 1 – 4×3 + 8×2 + 2×2 – 8x – 2×2 + 4x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 2×2 + x 2x – 4 4×3 – 6×2 – 8x + 1 – 4×3 + 8×2 + 2×2 – 8x – 2×2 + 4x – 4x
Pull the next terms from the original dividend down into the current dividend.
 2×2 + x 2x – 4 4×3 – 6×2 – 8x + 1 – 4×3 + 8×2 + 2×2 – 8x – 2×2 + 4x – 4x + 1
Divide the highest order term in the dividend -4x by the highest order term in divisor 2x.
 2×2 + x – 2 2x – 4 4×3 – 6×2 – 8x + 1 – 4×3 + 8×2 + 2×2 – 8x – 2×2 + 4x – 4x + 1
Multiply the new quotient term by the divisor.
 2×2 + x – 2 2x – 4 4×3 – 6×2 – 8x + 1 – 4×3 + 8×2 + 2×2 – 8x – 2×2 + 4x – 4x + 1 – 4x + 8
The expression needs to be subtracted from the dividend, so change all the signs in -4x+8
 2×2 + x – 2 2x – 4 4×3 – 6×2 – 8x + 1 – 4×3 + 8×2 + 2×2 – 8x – 2×2 + 4x – 4x + 1 + 4x – 8
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 2×2 + x – 2 2x – 4 4×3 – 6×2 – 8x + 1 – 4×3 + 8×2 + 2×2 – 8x – 2×2 + 4x – 4x + 1 + 4x – 8 – 7
The final answer is the quotient plus the remainder over the divisor.
2×2+x-2-72x-4
Divide (4x^3-6x^2-8x+1)/(2x-4)