Factor the following expression completely. x^(4)+2x^(3)-3x^(2)-25x^(2)-50 x+75 Answer:

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Factor the following expression completely.  x^(4)+2x^(3)-3x^(2)-25x^(2)-50 x+75 Answer:

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Combine Like Terms: First, we need to combine like terms in the expression. x^4 + 2x^3 - 3x^2 - 25x^2 - 50x + 75 Combine the x^2 terms: -3x^2 - 25x^2 = -28x^2 The expression becomes: x^4 + 2x^3 - 28x^2 - 50x + 75Factor by Grouping: Next, we look for common factors in groups of terms. Group the terms as follows: (x^4 + 2x^3) + (-28x^2 - 50x) + 75 Now factor by grouping. First group: x^3 is a common factor in x^4 + 2x^3, so factor it out. x^3(x + 2) Second group: -2 is a common factor in -28x^2 - 50x, so factor it out. -2(14x^2 + 25x) The expression now looks like this: x^3(x + 2) - 2(14x^2 + 25x) + 75Factor Quadratic Part: We notice that there is no common factor in the second group, and the factoring by grouping does not seem to work directly. Let's try to factor the quadratic part of the expression as if it were a separate quadratic equation. The quadratic part is x^4 + 2x^3 - 28x^2. Let's look for two numbers that multiply to give the product of the coefficient of x^4 (-1) and the constant term (-28) and add up to the coefficient of x^3 (2). The numbers are 4 and -7 because 4 * (-7) = -28 and 4 + (-7) = -2 (not 2, which indicates a mistake).

Factor the following expression completely. $\newline$ $x^{4}+2 x^{3}-3 x^{2}-25 x^{2}-50 x+75$ $\newline$ Answer:

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Factor the following expression completely.\newlinex4+2x3−3x2−25x2−50x+75 x^{4}+2 x^{3}-3 x^{2}-25 x^{2}-50 x+75 x4+2x3−3x2−25x2−50x+75\newlineAnswer:

Factor the following expression completely. $\newline$ $x^{4}+2 x^{3}-3 x^{2}-25 x^{2}-50 x+75$ $\newline$ Answer: