Divide (10x^3+8x^2+13x+4)÷(5x-1)

Math
(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.
5x110×3+8×2+13x+4
Divide the highest order term in the dividend 10×3 by the highest order term in divisor 5x.
2×2
5x110×3+8×2+13x+4
Multiply the new quotient term by the divisor.
2×2
5x110×3+8×2+13x+4
+10×32×2
The expression needs to be subtracted from the dividend, so change all the signs in 10×3-2×2
2×2
5x110×3+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
5x110×3+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
5x110×3+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
5x110×3+8×2+13x+4
10×3+2×2
+10×2+13x
Multiply the new quotient term by the divisor.
2×2+2x
5x110×3+8×2+13x+4
10×3+2×2
+10×2+13x
+10×22x
The expression needs to be subtracted from the dividend, so change all the signs in 10×2-2x
2×2+2x
5x110×3+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
5x110×3+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
5x110×3+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
5x110×3+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
5x110×3+8×2+13x+4
10×3+2×2
+10×2+13x
10×2+2x
+15x+4
+15x3
The expression needs to be subtracted from the dividend, so change all the signs in 15x-3
2×2+2x+3
5x110×3+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
5x110×3+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
Divide (10x^3+8x^2+13x+4)÷(5x-1)

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