Question

question
factor completely:
$3x^2 + 5x - 2$

Explanation:

Step1: Use AC method for factoring

For quadratic \(ax^{2}+bx + c\), find two numbers that multiply to \(a\times c\) and add to \(b\). Here, \(a = 3\), \(b = 5\), \(c=-2\), so \(a\times c=3\times(-2)= - 6\). We need two numbers that multiply to \(-6\) and add to \(5\). The numbers are \(6\) and \(-1\) since \(6\times(-1)=-6\) and \(6 + (-1)=5\).

Step2: Rewrite the middle term

Rewrite \(5x\) as \(6x - x\) in the quadratic: \(3x^{2}+6x - x - 2\).

Step3: Group and factor

Group the first two terms and the last two terms: \((3x^{2}+6x)+(-x - 2)\). Factor out the GCF from each group: \(3x(x + 2)-1(x + 2)\).

Step4: Factor out the common binomial

Factor out \((x + 2)\) from both terms: \((3x - 1)(x + 2)\).

Answer:

\((3x - 1)(x + 2)\)