Factor completely: x^(2)(x^(2)-10)-5x(x^(2)-10)-24(x^(2)-10) Answer:

Identify common factor: Identify the common factor in all terms of the expression. The common factor is (x^2 - 10). Factor out the common factor from the expression. x^2(x^2 - 10) - 5x(x^2 - 10) - 24(x^2 - 10) = (x^2 - 10)(x^2 - 5x - 24)Factor out common factor: Now, factor the quadratic expression x^2 - 5x - 24. To factor the quadratic, we look for two numbers that multiply to -24 and add to -5. The numbers -8 and 3 satisfy these conditions. So, we can write x^2 - 5x - 24 as (x - 8)(x + 3).Factor quadratic expression: Combine the factored quadratic with the common factor that was factored out earlier. The completely factored form of the expression is (x^2 - 10)(x - 8)(x + 3).

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Q. Factor completely:

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x^{2}\left(x^{2}-10\right)-5 x\left(x^{2}-10\right)-24\left(x^{2}-10\right)

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Answer:

Identify common factor: Identify the common factor in all terms of the expression. $\newline$ The common factor is $(x^2 - 10)$ . $\newline$ Factor out the common factor from the expression. $\newline$ $x^2(x^2 - 10) - 5x(x^2 - 10) - 24(x^2 - 10) = (x^2 - 10)(x^2 - 5x - 24)$
Factor out common factor: Now, factor the quadratic expression $x^2 - 5x - 24$ . To factor the quadratic, we look for two numbers that multiply to $-24$ and add to $-5$ . The numbers $-8$ and $3$ satisfy these conditions. So, we can write $x^2 - 5x - 24$ as $(x - 8)(x + 3)$ .
Factor quadratic expression: Combine the factored quadratic with the common factor that was factored out earlier. $\newline$ The completely factored form of the expression is $(x^2 - 10)(x - 8)(x + 3)$ .