How do you write $P (x) = x^{3} - 27 x - 54$ $P(x) = x^3 − 27x − 54$ in factored form?

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How do you write $P (x) = x^{3} - 27 x - 54$ $P(x) = x^3 − 27x − 54$ in factored form?

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Answer 1 · 2018-04-18T02:16:42

$x^{3} - 27 x - 54 = (x - 6) {(x + 3)}^{2}$ $x^3-27x-54=(x-6)(x+3)^2$

Explanation:

$x^{3} - 27 x - 54$ $x^3-27x-54$

First note that $P (- 3) = 0$ $P(-3)=0$ . This means that $x + 3$ $x+3$ is a factor of $P (x)$ $P(x)$ . Lets synthetically divide $P (x)$ $P(x)$ by $x + 3$ $x+3$ and see what remains.

$x^{3} - 27 x - 54 = x^{3} + 3 x^{2} - 3 x^{2} - 9 x - 18 x - 54$ $x^3-27x-54=x^3+3x^2-3x^2-9x-18x-54$

$= x^{2} (x + 3) - 3 x (x + 3) - 18 (x + 3)$ $=x^2(x+3)-3x(x+3)-18(x+3)$

$= (x^{2} - 3 x - 18) (x + 3)$ $=(x^2-3x-18)(x+3)$

$= (x - 6) (x + 3) (x + 3)$ $=(x-6)(x+3)(x+3)$

$= (x - 6) {(x + 3)}^{2}$ $=(x-6)(x+3)^2$

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How do you write $P (x) = x^{3} - 27 x - 54$ $P(x) = x^3 − 27x − 54$ in factored form?

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Explanation:

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How do you write P(x)=x3−27x−54P(x) = x^3 − 27x − 54 in factored form?

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How do you write $P (x) = x^{3} - 27 x - 54$ $P(x) = x^3 − 27x − 54$ in factored form?