Question

1. $x^2 + 9x + 14$ and $(x + 2)(x + \square)$

Explanation:

Step1: Recall factoring trinomials

To factor \(x^2 + bx + c\), we find two numbers that multiply to \(c\) and add to \(b\). Here, \(b = 9\), \(c = 14\).

Step2: Find two numbers for 14

We need two numbers that multiply to \(14\) and add to \(9\). The numbers are \(2\) and \(7\) (since \(2\times7 = 14\) and \(2 + 7 = 9\)).

Step3: Factor the trinomial

So, \(x^2 + 9x + 14=(x + 2)(x + 7)\).

Answer:

7