Solving Quadratic Equations by Factoring

Q1. Solve the equation by factoring: $x^2 + 5x + 6 = 0$

Background

Topic: Quadratic Equations and Factoring

This question tests your ability to solve a quadratic equation by factoring. Factoring is a method used to rewrite the quadratic equation as a product of two binomials set equal to zero, which allows you to find the solutions (roots) of the equation.

Key Terms and Formulas

• Quadratic Equation: An equation of the form $ax^2 + bx + c = 0$.

• Factoring: Rewriting an expression as a product of its factors.

• Zero Product Property: If $ab = 0$, then $a = 0$ or $b = 0$.

Step-by-Step Guidance

1. Identify the quadratic equation: $x^2 + 5x + 6 = 0$.

2. Look for two numbers that multiply to 6$(the constant term) and add up to $5$ (the coefficient of $x$).

3. Write the quadratic as a product of two binomials: $(x + m)(x + n) = 0$, where $m$ and $n$ are the numbers you found in the previous step.

4. Set each factor equal to zero: $x + m = 0$ and $x + n = 0$.

Try solving on your own before revealing the answer!