College Algebra CLEP Prep Practice Exam 2026 – The All-in-One Resource for Exam Success!

To solve the quadratic equation \( x^2 - 4x + 3 = 0 \), we can factor the left-hand side. The goal is to express the quadratic as a product of two binomials. We are looking for two numbers that multiply to the constant term, which is 3, and also add up to the coefficient of the linear term, which is -4.

The numbers that meet these criteria are -1 and -3, because:

- \( -1 \times -3 = 3 \)

- \( -1 + -3 = -4 \)

Using these numbers, we can factor the equation as follows:

\[

(x - 1)(x - 3) = 0

\]

Setting each factor equal to zero gives us the solutions to the equation:

1. \( x - 1 = 0 \) leads to \( x = 1 \)

2. \( x - 3 = 0 \) leads to \( x = 3 \)

This means the solutions to the original equation are \( x = 1 \) and \( x = 3 \). The correct answer should be the set of these solutions, which is {1, 3}.