Question

1. $x^2 + 3x - 28$ and $(x + \square)(x - \square)$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-28\) and add up to \(3\). Let's list factor pairs of \(-28\): \((-1,28)\), \((1,-28)\), \((-2,14)\), \((2,-14)\), \((-4,7)\), \((4,-7)\). Among these, \(7\) and \(-4\) satisfy \(7\times(-4)= -28\) and \(7 + (-4)=3\).

Step2: Factor the quadratic

Using the numbers found, we can factor \(x^{2}+3x - 28\) as \((x + 7)(x - 4)\).

Answer:

The first box is \(7\) and the second box is \(4\).