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Solve the following equation. x³+x²-4x-4=0

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Final answer:

To solve the equation x³+x²-4x-4=0, we can use the method of factoring to find the solutions: x = -1, x = 2, x = -2.

Step-by-step explanation:

To solve the equation x³+x²-4x-4=0, we can use the method of factoring. First, we group the terms in pairs:

x³+x²-4x-4 = (x³+x²) - (4x+4) = x²(x+1) - 4(x+1)

Now we can factor out the common factor of (x+1):

(x+1)(x²-4)

Then, we can further factor the quadratic expression x²-4 using the difference of squares:

(x+1)(x-2)(x+2)

Setting each factor equal to zero, we find the solutions: x = -1, x = 2, x = -2.

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