Question

multiple choice 1 point factor: ( x^2 + 9x + 14 ) ( \bigcirc (x + 9)(x + 14) ) ( \bigcirc (x + 7)(x + 2) ) ( \bigcirc (x + 14)(x + 1) ) ( \bigcirc (x - 7)(x - 2) ) previous

Explanation:

Step1: Identify $a,b,c$ for quadratic

For $x^2 + 9x + 14$, $a=1$, $b=9$, $c=14$

Step2: Find pair with sum $b$, product $ac$

Need two numbers: $7+2=9$, $7\times2=14$

Step3: Rewrite and factor by grouping

$$\begin{align*} x^2 + 7x + 2x + 14 &= x(x+7) + 2(x+7)\\ &=(x+7)(x+2) \end{align*}$$

Answer:

$\boldsymbol{(x+7)(x+2)}$ (the third option)