Divide (5x^4-10x^2+1)/(-3x^3+10x^2+500)

Math
5×4-10×2+1-3×3+10×2+500
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
3×3+10×2+0x+5005×4+0x310×2+0x+1
Divide the highest order term in the dividend 5×4 by the highest order term in divisor -3×3.
5×3
3×3+10×2+0x+5005×4+0x310×2+0x+1
Multiply the new quotient term by the divisor.
5×3
3×3+10×2+0x+5005×4+0x310×2+0x+1
+5×450×33+02500×3
The expression needs to be subtracted from the dividend, so change all the signs in 5×4-50×33+0-2500×3
5×3
3×3+10×2+0x+5005×4+0x310×2+0x+1
5×4+50×330+2500×3
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
5×3
3×3+10×2+0x+5005×4+0x310×2+0x+1
5×4+50×330+2500×3
+50×3310×2+2500×3
Pull the next terms from the original dividend down into the current dividend.
5×3
3×3+10×2+0x+5005×4+0x310×2+0x+1
5×4+50×330+2500×3
+50×3310×2+2500×3+1
Divide the highest order term in the dividend 50×33 by the highest order term in divisor -3×3.
5×3509
3×3+10×2+0x+5005×4+0x310×2+0x+1
5×4+50×330+2500×3
+50×3310×2+2500×3+1
Multiply the new quotient term by the divisor.
5×3509
3×3+10×2+0x+5005×4+0x310×2+0x+1
5×4+50×330+2500×3
+50×3310×2+2500×3+1
+50×33500×29+0250009
The expression needs to be subtracted from the dividend, so change all the signs in 50×33-500×29+0-250009
5×3509
3×3+10×2+0x+5005×4+0x310×2+0x+1
5×4+50×330+2500×3
+50×3310×2+2500×3+1
50×33+500×290+250009
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
5×3509
3×3+10×2+0x+5005×4+0x310×2+0x+1
5×4+50×330+2500×3
+50×3310×2+2500×3+1
50×33+500×290+250009
+410×29+2500×3+250099
The final answer is the quotient plus the remainder over the divisor.
-5×3-509+410×29+2500×3+250099-3×3+10×2+500
Divide (5x^4-10x^2+1)/(-3x^3+10x^2+500)

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