Factor the following expression completely. x^(4)-4x^(2)-8x^(3)+32 x+12x^(2)-48 Answer:

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Factor the following expression completely.  x^(4)-4x^(2)-8x^(3)+32 x+12x^(2)-48 Answer:

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Rewrite and Combine Terms: First, let's rewrite the expression in descending order of the powers of x: x^4 - 8x^3 + (12x^2 - 4x^2) + 32x - 48 Now, combine like terms: x^4 - 8x^3 + 8x^2 + 32x - 48Factor Out Common Factors: Next, we look for common factors in groups of terms. We can group the terms as follows: (x^4 - 8x^3) + (8x^2 + 32x) - 48 Now, factor out the greatest common factor from each group: x^3(x - 8) + 8x(x + 4) - 48Factor by Grouping: We notice that there is no common factor that we can factor out from all terms. However, we can try to factor by grouping. To do this, we need to find two numbers that multiply to give the product of the coefficient of x^4 (-1) and the constant term (-48), and add up to the coefficient of x^2 (8). These numbers are 12 and -4. So we rewrite the middle terms using 12 and -4: x^3(x - 8) + 12x(x - 8) - 4(x - 8)Factor Out Common Factor: Now, we can factor out the common factor (x - 8) from the terms: (x - 8)(x^3 + 12x - 4)Correct Mistake: We now have a quadratic in the form of x^3 + 12x - 4. This does not factor easily, and it seems we have made a mistake in the previous step because we should have a quadratic term, not a cubic term. We need to go back and correct this error.

Factor the following expression completely. $\newline$ $x^{4}-4 x^{2}-8 x^{3}+32 x+12 x^{2}-48$ $\newline$ Answer:

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Factor the following expression completely.\newlinex4−4x2−8x3+32x+12x2−48 x^{4}-4 x^{2}-8 x^{3}+32 x+12 x^{2}-48 x4−4x2−8x3+32x+12x2−48\newlineAnswer:

Factor the following expression completely. $\newline$ $x^{4}-4 x^{2}-8 x^{3}+32 x+12 x^{2}-48$ $\newline$ Answer: