Factor the following expression completely. x^(4)-16x^(2)-5x^(3)+80 x-6x^(2)+96 Answer:

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Factor the following expression completely.  x^(4)-16x^(2)-5x^(3)+80 x-6x^(2)+96 Answer:

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Rearrange Terms: First, we need to rearrange the terms of the expression in descending order of the powers of x. x^4 - 5x^3 - 16x^2 - 6x^2 + 80x + 96 Combine like terms. x^4 - 5x^3 - 22x^2 + 80x + 96Combine Like Terms: Next, we look for common factors in groups of terms. We can group the terms as follows: (x^4 - 5x^3) - (22x^2 - 80x) + 96 Now we factor by grouping.Group and Factor: Factor out the greatest common factor from each group. x^3(x - 5) - 22x(x - 4) + 96Further Factorization: We notice that the expression does not have a common factor in all terms, but we can look for a pattern or factors that can be factored further. The term +96 seems to be out of place, so we should check if we can factor the trinomial x^3(x - 5) - 22x(x - 4) further.Correct Mistake: Let's try to factor by splitting the middle term of the quadratic part of the expression. We are looking for two numbers that multiply to give -5 * -22 (the coefficient of x^4 times the constant term of the quadratic part) and add up to give the coefficient of the x term in the quadratic part, which is 0. However, we made a mistake in the previous step; the term +96 should have been included in the grouping. We need to correct this before proceeding.

Factor the following expression completely. $\newline$ $x^{4}-16 x^{2}-5 x^{3}+80 x-6 x^{2}+96$ $\newline$ Answer:

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Factor the following expression completely.\newlinex4−16x2−5x3+80x−6x2+96 x^{4}-16 x^{2}-5 x^{3}+80 x-6 x^{2}+96 x4−16x2−5x3+80x−6x2+96\newlineAnswer:

Factor the following expression completely. $\newline$ $x^{4}-16 x^{2}-5 x^{3}+80 x-6 x^{2}+96$ $\newline$ Answer: