Consider $8x^{2}+14x+3$. Factor the expression by grouping. First, the expression needs to be rewritten as $8x^{2}+ax+bx+3$. To find $a$ and $b$, set up a system to be solved.
$$a+b=14$$ $$ab=8\times 3=24$$
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 $14$.
$$a=2$$ $$b=12$$
Rewrite $8x^{2}+14x+3$ as $\left(8x^{2}+2x\right)+\left(12x+3\right)$.
$$\left(8x^{2}+2x\right)+\left(12x+3\right)$$
Factor out $2x$ in the first and $3$ in the second group.
$$2x\left(4x+1\right)+3\left(4x+1\right)$$
Factor out common term $4x+1$ by using distributive property.
