Question

1. $x^2 - 9x + 20$ and $(x - \square)(x - \square)$

Explanation:

Step1: Recall factoring quadratic

We need two numbers that multiply to \(20\) and add to \(-9\) (since the middle term is \(-9x\) and the constant term is \(20\)). The numbers are \(-4\) and \(-5\) because \((-4)\times(-5) = 20\) and \(-4 + (-5)=-9\).

Step2: Factor the quadratic

Using the formula \(x^{2}+bx + c=(x + m)(x + n)\) where \(m\) and \(n\) are the numbers we found, we get \(x^{2}-9x + 20=(x - 4)(x - 5)\).

Answer:

The first box is \(4\) and the second box is \(5\) (or vice - versa, since multiplication is commutative, \((x - 4)(x - 5)=(x - 5)(x - 4)\)).