Question

1. $x^2 - 12x - 28$ and $(x \square \square) (x \diamond \square)$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-28\) and add up to \(-12\). Let's list the factor pairs of \(-28\): \((-14, 2)\) because \(-14\times2 = -28\) and \(-14 + 2=-12\).

Step2: Factor the quadratic

Using the numbers we found, we can factor \(x^{2}-12x - 28\) as \((x - 14)(x + 2)\). So the first box (operation) for the first binomial is \(-\), the number is \(14\); the operation for the second binomial is \(+\), the number is \(2\).

Answer:

\((x - 14)(x + 2)\) (So the first square: \(-\), first rectangle: \(14\); the operation (diamond) is \(+\), second rectangle: \(2\))