(5x^4-3x^3+2x^2-1)/(x^2+4)
5x^2 -3x -18 +((12x+71)/(x^2+4))
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x^2 +4| 5x^4 -3x^3 +2x^2 +0x -1
-5x^4 -20x^2
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-3x^3 -18x^2 +0x -1
+3x^2 +12x
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-18x^2+12x -1
+18x^2 +72
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12x +71
Whoops, some of it didn't line up, but I used the long division method
To divide the polynomial (5x^4-3x^3+2x^2-1) by the polynomial (x^2+4), you can use long division.
Step 1: Arrange the polynomials in descending order of powers and fill in missing terms with zeros.
5x^4 - 3x^3 + 2x^2 - 1 (dividend)
÷ x^2 + 4 (divisor)
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5x^2
Step 2: Divide the first term of the dividend (5x^4) by the first term of the divisor (x^2) to get the first term of the quotient (5x^2).
5x^2 + ...
Step 3: Multiply the divisor (x^2 + 4) by the first term of the quotient (5x^2) and subtract the result from the dividend.
5x^2 * (x^2 + 4) = 5x^4 + 20x^2
(5x^4 - 3x^3 + 2x^2 - 1) - (5x^4 + 20x^2) = -3x^3 - 18x^2 - 1
Step 4: Bring down the next term of the dividend (-3x^3) and repeat steps 2 and 3 until you have completed the division.
5x^2 - 3
÷ x^2 + 4
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5x^2 + ...
5x^2 + 20
÷ x^2 + 4
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5x^2 - 3x + 2
- (5x^2 + 20)
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- 3x - 18
- (- 3x + 12)
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- 6
Step 5: Since the degree of the remainder (-6) is less than the degree of the divisor (x^2 + 4), the division is complete.
Therefore, the quotient is 5x^2 - 3 and the remainder is -6.