Answer
$(x+2)(2x+7)$
Work Step by Step
We use the quadratic formula to factor the polynomial $2x^2+11 x+14$ where $a=2,b=11, c=14$ as follows
$$
x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-11\pm\sqrt{11^2-4(2)(14)}}{2(2)}.$$
We get $x_1=-2$ and $x_2=-\frac{7}{2}$. Thus, one factor will be $x--2=x+2$ and the other will be $2x+7$ (which gives the root $-7/2$). That is
$$
2x^2+11 x+14=(x+2)(2x+7)$$
