Factor the following expression completely. x^(4)-16x^(2)-x^(3)+16 x-2x^(2)+32 Answer:

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Factor the following expression completely.  x^(4)-16x^(2)-x^(3)+16 x-2x^(2)+32 Answer:

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Rearrange and Combine Terms: First, let's rearrange the terms of the expression in descending order of the powers of x. x^4 - x^3 - 16x^2 - 2x^2 + 16x + 32 Combine like terms. x^4 - x^3 - 18x^2 + 16x + 32Look for Common Factors: Now, let's look for common factors in groups of terms. Group the terms as follows: (x^4 - x^3) + (-18x^2 + 16x) + 32 Factor out the common factor x^3 from the first group and 2x from the second group. x^3(x - 1) - 2x(9x - 8) + 32Factor by Grouping: We notice that there is no common factor that we can factor out from all terms, but we can look for a pattern or try to factor by grouping. Let's try to factor by grouping by rearranging the terms again: (x^4 - x^3) - (18x^2 - 16x) + 32 Factor out x^3 from the first group and 2x from the second group. x^3(x - 1) - 2x(9x - 8) + 32Factor by Grouping in Pairs: Now, we look for a common binomial factor between the groups. We can see that there is no common binomial factor, which means we need to try a different approach. Let's try to factor by grouping in pairs: (x^4 - 16x^2) - (x^3 - 16x) - (2x^2 - 32) Factor out x^2 from the first pair and x from the second pair. x^2(x^2 - 16) - x(x^2 - 16) - 2(x^2 - 16)Identify Common Factor: Now we can see that (x^2 - 16) is a common factor. Factor out (x^2 - 16) from each group. (x^2 - 16)(x^2 - x - 2)Factor Difference of Squares: The expression x^2 - 16 is a difference of squares and can be factored further. Factor x^2 - 16 into (x + 4)(x - 4). (x + 4)(x - 4)(x^2 - x - 2)Factor Quadratic: The quadratic x^2 - x - 2 can be factored into two binomials. Factor x^2 - x - 2 into (x - 2)(x + 1). (x + 4)(x - 4)(x - 2)(x + 1)

Factor the following expression completely. $\newline$ $x^{4}-16 x^{2}-x^{3}+16 x-2 x^{2}+32$ $\newline$ Answer:

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Factor the following expression completely.\newlinex4−16x2−x3+16x−2x2+32 x^{4}-16 x^{2}-x^{3}+16 x-2 x^{2}+32 x4−16x2−x3+16x−2x2+32\newlineAnswer:

Factor the following expression completely. $\newline$ $x^{4}-16 x^{2}-x^{3}+16 x-2 x^{2}+32$ $\newline$ Answer: