(X^4+3x^3-5x^2-5x-4):(x+4)

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To perform polynomial long division, we'll follow these steps:

Divide the first term of the dividend by the first term of the divisor. This gives us our first term of the quotient.Multiply the whole divisor by that number and subtract from the dividend.Bring down the next term of the dividend and repeat the process until all terms are used.

Here is the polynomial long division for (X^4 + 3x^3 - 5x^2 - 5x - 4) ÷ (x + 4):

X^3 - x^2 + 3x - 17

x + 4 | X^4 + 3x^3 - 5x^2 - 5x - 4

(X^4 + 4x^3)
- x^3 + 5x^2
- (x^3 + 4x^2) x^2 - 5x
- (x^2 + 4x) -9x - 4
- (-9x - 36) 32

Therefore, (X^4 + 3x^3 - 5x^2 - 5x - 4) ÷ (x + 4) = X^3 - x^2 + 3x - 9 with a remainder of 32.