Question

1. $x^2 - 7x + 12 = (x - __)(x - __)$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(12\) (the constant term) and add up to \(-7\) (the coefficient of \(x\) with a sign change, since the middle term is \(-7x\) and in the factored form \((x - a)(x - b)=x^2-(a + b)x+ab\)). The numbers are \(-3\) and \(-4\) because \((-3)\times(-4) = 12\) and \((-3)+(-4)=-7\).

Step2: Factor the quadratic

Using the two numbers, we can factor \(x^{2}-7x + 12\) as \((x - 3)(x - 4)\).

Answer:

The first blank is \(3\) and the second blank is \(4\), so the factored form is \((x - 3)(x - 4)\).