How do you factor $2 x^{3} + 7 x^{2} - 17 x - 10$ $2x^3+7x^2-17x-10$ ?

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How do you factor $2 x^{3} + 7 x^{2} - 17 x - 10$ $2x^3+7x^2-17x-10$ ?

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Answer 1 · 2015-05-23T03:39:56

$f (x) = 2 x^{3} + 7 x - 17 x - 10$ $f(x) = 2x^3 + 7x - 17x - 10$

First try x = 2 -> f(x) = 0, then one factor is (x - 2). Next, divide or guess.

$f (x) = (x - 2) (2 x^{2} + 11 x + 5)$ $f(x) = (x - 2)(2x^2 + 11x +5)$

Check by developing:
$f (x) = 2 x^{3} + 11 x^{2} + 5 x - 4 x^{2} - 22 x - 10 = 2 x^{3} + 7 x^{2} - 17 x - 10$ $f(x) = 2x^3 + 11x^2 + 5x - 4x^2 - 22x - 10 = 2x^3 + 7x^2 - 17x - 10$ .

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How do you factor $2 x^{3} + 7 x^{2} - 17 x - 10$ $2x^3+7x^2-17x-10$ ?

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