Factor completely: x^(3)-17x^(2)+72 x Answer:

Identify common factors: Identify common factors in all terms of the polynomial x^3 - 17x^2 + 72x. All terms have an x in common, so we can factor out x. x(x^2 - 17x + 72)Factor quadratic expression: Factor the quadratic expression x^2 - 17x + 72. We need to find two numbers that multiply to 72 and add up to -17. These numbers are -8 and -9. x(x - 8)(x - 9)Check factored form: Check the factored form by expanding it to ensure it matches the original polynomial. x(x - 8)(x - 9) = x(x^2 - 9x - 8x + 72) = x(x^2 - 17x + 72) = x^3 - 17x^2 + 72x The expanded form matches the original polynomial, so the factoring is correct.

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Factor completely:

x^(3)-17x^(2)+72 x
Answer:

Factor completely: $\newline$ $x^{3}-17 x^{2}+72 x$ $\newline$ Answer:

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Q. Factor completely:

\newline

x^{3}-17 x^{2}+72 x

\newline

Answer:

Identify common factors: Identify common factors in all terms of the polynomial $x^3 - 17x^2 + 72x$ . All terms have an $x$ in common, so we can factor out $x$ . $x(x^2 - 17x + 72)$
Factor quadratic expression: Factor the quadratic expression $x^2 - 17x + 72$ . We need to find two numbers that multiply to $72$ and add up to $-17$ . These numbers are $-8$ and $-9$ . $x(x - 8)(x - 9)$
Check factored form: Check the factored form by expanding it to ensure it matches the original polynomial. $\newline$ $x(x - 8)(x - 9) = x(x^2 - 9x - 8x + 72) = x(x^2 - 17x + 72) = x^3 - 17x^2 + 72x$ $\newline$ The expanded form matches the original polynomial, so the factoring is correct.