How do you factor the trinomial $2 x^{2} + 3 x - 2$ $2x ^2 + 3x - 2$ ?

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Answer 1 · 2016-01-09T02:23:00

In order to factor trinomials of the form $a x^{2}$ $ax^2$ + bx + c, a $\neq$ $!=$ 1, find two numbers that multiply to ac and that add to b.

$2 x^{2}$ $2x^2$ + 3x - 2

Two numbers that multiply to -4 and add to +3 are 4 and -1:

= $2 x^{2}$ $2x^2$ + 4x - x - 2

= 2x(x + 2) - 1(x + 2)

= (2x - 1)(x + 2)

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