Question

question
factor completely.
$2x^2 + 3x - 2$

Explanation:

Step1: Use the AC method for factoring quadratic trinomials. For the quadratic \(ax^{2}+bx + c\) (here \(a = 2\), \(b = 3\), \(c=- 2\)), first find \(ac=2\times(-2)=-4\).

Step2: Find two numbers that multiply to -4 and add up to \(b = 3\). The numbers are 4 and -1 (since \(4\times(-1)=-4\) and \(4+( - 1)=3\)).

Step3: Rewrite the middle term using these two numbers: \(2x^{2}+4x - x - 2\).

Step4: Group the first two terms and the last two terms: \((2x^{2}+4x)+(-x - 2)\).

Step5: Factor out the greatest common factor from each group: \(2x(x + 2)-1(x + 2)\).

Step6: Factor out the common binomial factor \((x + 2)\): \((2x-1)(x + 2)\).

Answer:

\((2x - 1)(x + 2)\)