How do you factor $2x^3 + 7x^2 - 3x -18$ ?

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How do you factor $2x^3 + 7x^2 - 3x -18$ ?

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Answer 1 · 2015-05-10T17:36:38

$2x^3+7x^2-3x-18=(x+3)(x+2)(2x-3)$

The $2x^3$ term quickly becomes dominant as $|x|$ increases, so any solutions of $2x^3+7x^2-3x-18 = 0$ will be quite small.

Integer solutions will be factors of 18, so try $x = -3, -2, -1, 0, 1, 2 or 3$ . $x = -3$ is a solution, so $(x + 3)$ is a factor. $x = -2$ is also a solution, so $(x+2)$ is also a factor. If the remaining factor is of the form $(ax+b)$ then looking at the coefficient of $x^3$ ( $2$ ) and the constant term ( $18$ ) we must have $a=2$ and $b=-3$ .

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How do you factor $2x^3 + 7x^2 - 3x -18$ ?

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