Factor the following expression completely. x^(4)-4x^(2)-7x^(3)+28 x+10x^(2)-40 Answer:

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Factor the following expression completely.  x^(4)-4x^(2)-7x^(3)+28 x+10x^(2)-40 Answer:

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Rearrange terms in descending order: First, we should rearrange the terms of the polynomial in descending order of the powers of x. x^4 - 7x^3 + 6x^2 + 28x - 40Look for common factors: Next, we look for common factors in groups of terms. We can group the terms as follows: (x^4 - 7x^3) + (6x^2 + 28x) - 40.Factor by grouping: Factor by grouping. For the first group (x^4 - 7x^3), we can factor out an x^3, and for the second group (6x^2 + 28x), we can factor out a 2x. This gives us: x^3(x - 7) + 2x(3x + 14) - 40Find common factor: We notice that the term 40 does not have a common factor with the other groups. However, we can still look for a common factor between the terms x^3(x - 7) and 2x(3x + 14). We see that there is no common factor, so we need to look for a different approach to factor the expression completely.Try different grouping: Let's try to factor by grouping in a different way. We can rearrange the terms to see if there's a better grouping: x^4 - 7x^3 + 10x^2 - 4x^2 + 28x - 40 Now, we group them as follows: (x^4 - 7x^3 + 10x^2) + (-4x^2 + 28x - 40).Factor by grouping again: For the first group (x^4 - 7x^3 + 10x^2), we can factor out an x^2, and for the second group (-4x^2 + 28x - 40), we can factor out a -4. This gives us: x^2(x^2 - 7x + 10) - 4(x^2 - 7x + 10)Factor out common factor: We now have a common factor of (x^2 - 7x + 10) in both groups. We can factor this out: (x^2 - 7x + 10)(x^2 - 4)Factor simple trinomial: The quadratic x^2 - 7x + 10 can be factored further since it is a simple trinomial. We look for two numbers that multiply to 10 and add up to -7. These numbers are -5 and -2. So we can write: (x - 5)(x - 2)(x^2 - 4)Factor difference of squares: The term x^2 - 4 is a difference of squares and can be factored as (x + 2)(x - 2). So the fully factored form of the expression is: (x - 5)(x - 2)(x + 2)(x - 2)Final fully factored form: We notice that (x - 2) is repeated, so we can write it with an exponent: (x - 5)(x - 2)^2(x + 2) This is the completely factored form of the expression.

Factor the following expression completely. $\newline$ $x^{4}-4 x^{2}-7 x^{3}+28 x+10 x^{2}-40$ $\newline$ Answer:

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Factor the following expression completely.\newlinex4−4x2−7x3+28x+10x2−40 x^{4}-4 x^{2}-7 x^{3}+28 x+10 x^{2}-40 x4−4x2−7x3+28x+10x2−40\newlineAnswer:

Factor the following expression completely. $\newline$ $x^{4}-4 x^{2}-7 x^{3}+28 x+10 x^{2}-40$ $\newline$ Answer: