# Divide (3x^3+8x^2-10x-24)/(x+4)

3×3+8×2-10x-24x+4
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
 x + 4 3×3 + 8×2 – 10x – 24
Divide the highest order term in the dividend 3×3 by the highest order term in divisor x.
 3×2 x + 4 3×3 + 8×2 – 10x – 24
Multiply the new quotient term by the divisor.
 3×2 x + 4 3×3 + 8×2 – 10x – 24 + 3×3 + 12×2
The expression needs to be subtracted from the dividend, so change all the signs in 3×3+12×2
 3×2 x + 4 3×3 + 8×2 – 10x – 24 – 3×3 – 12×2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 3×2 x + 4 3×3 + 8×2 – 10x – 24 – 3×3 – 12×2 – 4×2
Pull the next terms from the original dividend down into the current dividend.
 3×2 x + 4 3×3 + 8×2 – 10x – 24 – 3×3 – 12×2 – 4×2 – 10x
Divide the highest order term in the dividend -4×2 by the highest order term in divisor x.
 3×2 – 4x x + 4 3×3 + 8×2 – 10x – 24 – 3×3 – 12×2 – 4×2 – 10x
Multiply the new quotient term by the divisor.
 3×2 – 4x x + 4 3×3 + 8×2 – 10x – 24 – 3×3 – 12×2 – 4×2 – 10x – 4×2 – 16x
The expression needs to be subtracted from the dividend, so change all the signs in -4×2-16x
 3×2 – 4x x + 4 3×3 + 8×2 – 10x – 24 – 3×3 – 12×2 – 4×2 – 10x + 4×2 + 16x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 3×2 – 4x x + 4 3×3 + 8×2 – 10x – 24 – 3×3 – 12×2 – 4×2 – 10x + 4×2 + 16x + 6x
Pull the next terms from the original dividend down into the current dividend.
 3×2 – 4x x + 4 3×3 + 8×2 – 10x – 24 – 3×3 – 12×2 – 4×2 – 10x + 4×2 + 16x + 6x – 24
Divide the highest order term in the dividend 6x by the highest order term in divisor x.
 3×2 – 4x + 6 x + 4 3×3 + 8×2 – 10x – 24 – 3×3 – 12×2 – 4×2 – 10x + 4×2 + 16x + 6x – 24
Multiply the new quotient term by the divisor.
 3×2 – 4x + 6 x + 4 3×3 + 8×2 – 10x – 24 – 3×3 – 12×2 – 4×2 – 10x + 4×2 + 16x + 6x – 24 + 6x + 24
The expression needs to be subtracted from the dividend, so change all the signs in 6x+24
 3×2 – 4x + 6 x + 4 3×3 + 8×2 – 10x – 24 – 3×3 – 12×2 – 4×2 – 10x + 4×2 + 16x + 6x – 24 – 6x – 24
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 3×2 – 4x + 6 x + 4 3×3 + 8×2 – 10x – 24 – 3×3 – 12×2 – 4×2 – 10x + 4×2 + 16x + 6x – 24 – 6x – 24 – 48
The final answer is the quotient plus the remainder over the divisor.
3×2-4x+6-48x+4
Divide (3x^3+8x^2-10x-24)/(x+4)