College Math Placement Practice Test 2026 - Free College Math Questions and Study Guide

To determine why the expression (x - 2)(x - 3) correctly represents the quadratic equation x^2 - 5x + 6 = 0, we need to factor the quadratic.

A quadratic equation can be factored into the form (x - p)(x - q), where p and q are the roots of the equation. We can find p and q by looking for two numbers that multiply to give the constant term (6 in this case) and add up to give the coefficient of the x term (-5).

The numbers 2 and 3 meet these criteria:

- Their product is 2 * 3 = 6.

- Their sum is 2 + 3 = 5, but we need -5 for the equation, which means we can rewrite the factors as (x - 2)(x - 3).

When we expand (x - 2)(x - 3), we get:

1. x(x - 3) - 2(x - 3) which simplifies to x^2 - 3x - 2x + 6.

2. This further simplifies to x^2 - 5x + 6.

Thus, the expression (x