# Divide (6x^2+21x+6)/(2x+5)

6×2+21x+62x+5
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
 2x + 5 6×2 + 21x + 6
Divide the highest order term in the dividend 6×2 by the highest order term in divisor 2x.
 3x 2x + 5 6×2 + 21x + 6
Multiply the new quotient term by the divisor.
 3x 2x + 5 6×2 + 21x + 6 + 6×2 + 15x
The expression needs to be subtracted from the dividend, so change all the signs in 6×2+15x
 3x 2x + 5 6×2 + 21x + 6 – 6×2 – 15x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 3x 2x + 5 6×2 + 21x + 6 – 6×2 – 15x + 6x
Pull the next terms from the original dividend down into the current dividend.
 3x 2x + 5 6×2 + 21x + 6 – 6×2 – 15x + 6x + 6
Divide the highest order term in the dividend 6x by the highest order term in divisor 2x.
 3x + 3 2x + 5 6×2 + 21x + 6 – 6×2 – 15x + 6x + 6
Multiply the new quotient term by the divisor.
 3x + 3 2x + 5 6×2 + 21x + 6 – 6×2 – 15x + 6x + 6 + 6x + 15
The expression needs to be subtracted from the dividend, so change all the signs in 6x+15
 3x + 3 2x + 5 6×2 + 21x + 6 – 6×2 – 15x + 6x + 6 – 6x – 15
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 3x + 3 2x + 5 6×2 + 21x + 6 – 6×2 – 15x + 6x + 6 – 6x – 15 – 9
The final answer is the quotient plus the remainder over the divisor.
3x+3-92x+5
Divide (6x^2+21x+6)/(2x+5)