# Divide (4x^3-12x+11)/(2x-2)

4×3-12x+112x-2
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
 2x – 2 4×3 + 0x2 – 12x + 11
Divide the highest order term in the dividend 4×3 by the highest order term in divisor 2x.
 2×2 2x – 2 4×3 + 0x2 – 12x + 11
Multiply the new quotient term by the divisor.
 2×2 2x – 2 4×3 + 0x2 – 12x + 11 + 4×3 – 4×2
The expression needs to be subtracted from the dividend, so change all the signs in 4×3-4×2
 2×2 2x – 2 4×3 + 0x2 – 12x + 11 – 4×3 + 4×2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 2×2 2x – 2 4×3 + 0x2 – 12x + 11 – 4×3 + 4×2 + 4×2
Pull the next terms from the original dividend down into the current dividend.
 2×2 2x – 2 4×3 + 0x2 – 12x + 11 – 4×3 + 4×2 + 4×2 – 12x
Divide the highest order term in the dividend 4×2 by the highest order term in divisor 2x.
 2×2 + 2x 2x – 2 4×3 + 0x2 – 12x + 11 – 4×3 + 4×2 + 4×2 – 12x
Multiply the new quotient term by the divisor.
 2×2 + 2x 2x – 2 4×3 + 0x2 – 12x + 11 – 4×3 + 4×2 + 4×2 – 12x + 4×2 – 4x
The expression needs to be subtracted from the dividend, so change all the signs in 4×2-4x
 2×2 + 2x 2x – 2 4×3 + 0x2 – 12x + 11 – 4×3 + 4×2 + 4×2 – 12x – 4×2 + 4x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 2×2 + 2x 2x – 2 4×3 + 0x2 – 12x + 11 – 4×3 + 4×2 + 4×2 – 12x – 4×2 + 4x – 8x
Pull the next terms from the original dividend down into the current dividend.
 2×2 + 2x 2x – 2 4×3 + 0x2 – 12x + 11 – 4×3 + 4×2 + 4×2 – 12x – 4×2 + 4x – 8x + 11
Divide the highest order term in the dividend -8x by the highest order term in divisor 2x.
 2×2 + 2x – 4 2x – 2 4×3 + 0x2 – 12x + 11 – 4×3 + 4×2 + 4×2 – 12x – 4×2 + 4x – 8x + 11
Multiply the new quotient term by the divisor.
 2×2 + 2x – 4 2x – 2 4×3 + 0x2 – 12x + 11 – 4×3 + 4×2 + 4×2 – 12x – 4×2 + 4x – 8x + 11 – 8x + 8
The expression needs to be subtracted from the dividend, so change all the signs in -8x+8
 2×2 + 2x – 4 2x – 2 4×3 + 0x2 – 12x + 11 – 4×3 + 4×2 + 4×2 – 12x – 4×2 + 4x – 8x + 11 + 8x – 8
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 2×2 + 2x – 4 2x – 2 4×3 + 0x2 – 12x + 11 – 4×3 + 4×2 + 4×2 – 12x – 4×2 + 4x – 8x + 11 + 8x – 8 + 3
The final answer is the quotient plus the remainder over the divisor.
2×2+2x-4+32x-2
Divide (4x^3-12x+11)/(2x-2)