Factor the expression by grouping. First, the expression needs to be rewritten as $3x^{2}+ax+bx+8$. To find $a$ and $b$, set up a system to be solved.
$$a+b=10$$ $$ab=3\times 8=24$$
Since $ab$ is positive, $a$ and $b$ have the same sign. Since $a+b$ is positive, $a$ and $b$ are both positive. List all such integer pairs that give product $24$.
$$1,24$$ $$2,12$$ $$3,8$$ $$4,6$$
Calculate the sum for each pair.
$$1+24=25$$ $$2+12=14$$ $$3+8=11$$ $$4+6=10$$
The solution is the pair that gives sum $10$.
$$a=4$$ $$b=6$$
Rewrite $3x^{2}+10x+8$ as $\left(3x^{2}+4x\right)+\left(6x+8\right)$.
$$\left(3x^{2}+4x\right)+\left(6x+8\right)$$
Factor out $x$ in the first and $2$ in the second group.
$$x\left(3x+4\right)+2\left(3x+4\right)$$
Factor out common term $3x+4$ by using distributive property.
