Factor the expression by grouping. First, the expression needs to be rewritten as $12x^{2}+ax+bx-2$. To find $a$ and $b$, set up a system to be solved.
$$a+b=5$$ $$ab=12\left(-2\right)=-24$$
Since $ab$ is negative, $a$ and $b$ have the opposite signs. Since $a+b$ is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product $-24$.
$$-1,24$$ $$-2,12$$ $$-3,8$$ $$-4,6$$
Calculate the sum for each pair.
$$-1+24=23$$ $$-2+12=10$$ $$-3+8=5$$ $$-4+6=2$$
The solution is the pair that gives sum $5$.
$$a=-3$$ $$b=8$$
Rewrite $12x^{2}+5x-2$ as $\left(12x^{2}-3x\right)+\left(8x-2\right)$.
$$\left(12x^{2}-3x\right)+\left(8x-2\right)$$
Factor out $3x$ in the first and $2$ in the second group.
$$3x\left(4x-1\right)+2\left(4x-1\right)$$
Factor out common term $4x-1$ by using distributive property.
