# Divide (10x^3+8x^2+13x+4)÷(5x-1) (10×3+8×2+13x+4)÷(5x-1)
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
 5x – 1 10×3 + 8×2 + 13x + 4
Divide the highest order term in the dividend 10×3 by the highest order term in divisor 5x.
 2×2 5x – 1 10×3 + 8×2 + 13x + 4
Multiply the new quotient term by the divisor.
 2×2 5x – 1 10×3 + 8×2 + 13x + 4 + 10×3 – 2×2
The expression needs to be subtracted from the dividend, so change all the signs in 10×3-2×2
 2×2 5x – 1 10×3 + 8×2 + 13x + 4 – 10×3 + 2×2
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 2×2 5x – 1 10×3 + 8×2 + 13x + 4 – 10×3 + 2×2 + 10×2
Pull the next terms from the original dividend down into the current dividend.
 2×2 5x – 1 10×3 + 8×2 + 13x + 4 – 10×3 + 2×2 + 10×2 + 13x
Divide the highest order term in the dividend 10×2 by the highest order term in divisor 5x.
 2×2 + 2x 5x – 1 10×3 + 8×2 + 13x + 4 – 10×3 + 2×2 + 10×2 + 13x
Multiply the new quotient term by the divisor.
 2×2 + 2x 5x – 1 10×3 + 8×2 + 13x + 4 – 10×3 + 2×2 + 10×2 + 13x + 10×2 – 2x
The expression needs to be subtracted from the dividend, so change all the signs in 10×2-2x
 2×2 + 2x 5x – 1 10×3 + 8×2 + 13x + 4 – 10×3 + 2×2 + 10×2 + 13x – 10×2 + 2x
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 2×2 + 2x 5x – 1 10×3 + 8×2 + 13x + 4 – 10×3 + 2×2 + 10×2 + 13x – 10×2 + 2x + 15x
Pull the next terms from the original dividend down into the current dividend.
 2×2 + 2x 5x – 1 10×3 + 8×2 + 13x + 4 – 10×3 + 2×2 + 10×2 + 13x – 10×2 + 2x + 15x + 4
Divide the highest order term in the dividend 15x by the highest order term in divisor 5x.
 2×2 + 2x + 3 5x – 1 10×3 + 8×2 + 13x + 4 – 10×3 + 2×2 + 10×2 + 13x – 10×2 + 2x + 15x + 4
Multiply the new quotient term by the divisor.
 2×2 + 2x + 3 5x – 1 10×3 + 8×2 + 13x + 4 – 10×3 + 2×2 + 10×2 + 13x – 10×2 + 2x + 15x + 4 + 15x – 3
The expression needs to be subtracted from the dividend, so change all the signs in 15x-3
 2×2 + 2x + 3 5x – 1 10×3 + 8×2 + 13x + 4 – 10×3 + 2×2 + 10×2 + 13x – 10×2 + 2x + 15x + 4 – 15x + 3
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
 2×2 + 2x + 3 5x – 1 10×3 + 8×2 + 13x + 4 – 10×3 + 2×2 + 10×2 + 13x – 10×2 + 2x + 15x + 4 – 15x + 3 + 7
The final answer is the quotient plus the remainder over the divisor.
2×2+2x+3+75x-1
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