Question

factor.\\(v^2 + 10v + 9\\)

Explanation:

Step1: Find pair summing to 10, product 9

We need two numbers that add to 10 and multiply to 9: 1 and 9.

Step2: Split middle term and factor

Rewrite the quadratic as $v^2 + v + 9v + 9$, then factor by grouping:

$$\begin{align*} v^2 + v + 9v + 9 &= v(v+1) + 9(v+1) \\ &= (v+1)(v+9) \end{align*}$$

Answer:

$(v+1)(v+9)$