How do you factor $x^{4} + 6 x^{3} - 36 x^{2} - 216 x$ $x^4+6x^3-36x^2-216x$ ?

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How do you factor $x^{4} + 6 x^{3} - 36 x^{2} - 216 x$ $x^4+6x^3-36x^2-216x$ ?

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Answer 1 · 2017-05-22T09:05:56

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

Explanation:

$x^{4} + 6 x^{3} - 36 x^{2} - 216 x$ $x^4+6x^3-36x^2-216x$

$= x (x^{3} + 6 x^{2} - 36 x - 216) \leftarrow common factor x$ $=x(x^3+6x^2-36x-216)larr" common factor " x$

$note that when x = 6$ $"note that when " x=6$

$x^{3} + 6 x^{2} - 36 x - 216 = 0$ $x^3+6x^2-36x-216=0$

$\Rightarrow x = 6 is a root and hence (x - 6) is a factor$ $rArrx=6" is a root and hence " (x-6)" is a factor"$

$\Rightarrow x^{2} (x - 6) + 12 x (x - 6) + 36 (x - 6)$ $rArrx^2(x-6)+12x(x-6)+36(x-6)$

$= (x - 6) (x^{2} + 12 x + 36)$ $=(x-6)(x^2+12x+36)$

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

$\Rightarrow x^{4} + 6 x^{3} - 36 x^{2} - 216 x = x (x - 6) {(x + 6)}^{2}$ $rArrx^4+6x^3-36x^2-216x=x(x-6)(x+6)^2$

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How do you factor $x^{4} + 6 x^{3} - 36 x^{2} - 216 x$ $x^4+6x^3-36x^2-216x$ ?

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How do you factor x^4+6x^3-36x^2-216xx4+6x3−36x2−216xx^4+6x^3-36x^2-216x?

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How do you factor $x^{4} + 6 x^{3} - 36 x^{2} - 216 x$ $x^4+6x^3-36x^2-216x$ ?