# Divide (15x^2+24x+1)/(5x+3)

15×2+24x+15x+3
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
 5x + 3 15×2 + 24x + 1
Divide the highest order term in the dividend 15×2 by the highest order term in divisor 5x.
 3x 5x + 3 15×2 + 24x + 1
Multiply the new quotient term by the divisor.
 3x 5x + 3 15×2 + 24x + 1 + 15×2 + 9x
The expression needs to be subtracted from the dividend, so change all the signs in 15×2+9x
 3x 5x + 3 15×2 + 24x + 1 – 15×2 – 9x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 3x 5x + 3 15×2 + 24x + 1 – 15×2 – 9x + 15x
Pull the next terms from the original dividend down into the current dividend.
 3x 5x + 3 15×2 + 24x + 1 – 15×2 – 9x + 15x + 1
Divide the highest order term in the dividend 15x by the highest order term in divisor 5x.
 3x + 3 5x + 3 15×2 + 24x + 1 – 15×2 – 9x + 15x + 1
Multiply the new quotient term by the divisor.
 3x + 3 5x + 3 15×2 + 24x + 1 – 15×2 – 9x + 15x + 1 + 15x + 9
The expression needs to be subtracted from the dividend, so change all the signs in 15x+9
 3x + 3 5x + 3 15×2 + 24x + 1 – 15×2 – 9x + 15x + 1 – 15x – 9
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 3x + 3 5x + 3 15×2 + 24x + 1 – 15×2 – 9x + 15x + 1 – 15x – 9 – 8
The final answer is the quotient plus the remainder over the divisor.
3x+3-85x+3
Divide (15x^2+24x+1)/(5x+3)