What are the factors for $6 w^{3} + 30 w^{2} - 18 w - 90 = 0$ $6w^3 + 30w^2 -18w - 90 = 0$ ?

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What are the factors for $6 w^{3} + 30 w^{2} - 18 w - 90 = 0$ $6w^3 + 30w^2 -18w - 90 = 0$ ?

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Answer 1 · 2015-05-09T00:25:13

$6 w^{3} + 30 w^{2} - 18 w - 90 = 0$ $6w^3+30w^2 - 18w-90 = 0$

Grouping
$(6 w^{3} + 30 w^{2}) - (18 w + 90) = 0$ $color(red)((6w^3+30w^2)) - color(blue)((18w+90)) = 0$

$(6 w^{2}) (w + 5) - (18) (w + 5)$ $color(red)((6w^2)(w+5)) - color(blue)((18)(w+5))$

$(6 x^{2} - 18) (w + 5)$ $(6x^2-18)(w+5)$

Final check for other obvious common factors:
$6 (x^{2} - 3) (w + 5)$ $6(x^2-3)(w+5)$

$(x^{2} - 3)$ $(x^2-3)$ could be factored as $(x + \sqrt{3}) (x - \sqrt{3})$ $(x+sqrt(3))(x-sqrt(3))$ but it is not obvious that this would be any clearer.

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What are the factors for $6 w^{3} + 30 w^{2} - 18 w - 90 = 0$ $6w^3 + 30w^2 -18w - 90 = 0$ ?

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What are the factors for 6w3+30w2−18w−90=06w^3 + 30w^2 -18w - 90 = 0?

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What are the factors for $6 w^{3} + 30 w^{2} - 18 w - 90 = 0$ $6w^3 + 30w^2 -18w - 90 = 0$ ?