Factor completely: x^(2)(x^(2)-10)-5x(x^(2)-10)-14(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 Common Factor: Factor out the common factor from each term. x^2(x^2 - 10) - 5x(x^2 - 10) - 14(x^2 - 10) = (x^2 - 10)(x^2 - 5x - 14)Factor Quadratic Expression: Now, factor the quadratic expression (x^2 - 5x - 14). To factor the quadratic, we look for two numbers that multiply to -14 and add up to -5. These numbers are -7 and +2.Write Factored Form: Write the factored form of the quadratic expression. (x^2 - 5x - 14) = (x - 7)(x + 2)Combine Factored Expressions: Combine the factored quadratic with the common factor that was factored out earlier. (x^2 - 10)(x^2 - 5x - 14) = (x^2 - 10)(x - 7)(x + 2)

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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)-14\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 $(x^2 - 10)$ .
Factor Out Common Factor: Factor out the common factor from each term. $\newline$ $x^2(x^2 - 10) - 5x(x^2 - 10) - 14(x^2 - 10) = (x^2 - 10)(x^2 - 5x - 14)$
Factor Quadratic Expression: Now, factor the quadratic expression $x^2 - 5x - 14$ . To factor the quadratic, we look for two numbers that multiply to $-14$ and add up to $-5$ . These numbers are $-7$ and $+2$ .
Write Factored Form: Write the factored form of the quadratic expression. $\newline$ $(x^2 - 5x - 14) = (x - 7)(x + 2)$
Combine Factored Expressions: Combine the factored quadratic with the common factor that was factored out earlier. $\newline$ $(x^2 - 10)(x^2 - 5x - 14) = (x^2 - 10)(x - 7)(x + 2)$