Factoring is a method used to solve quadratic equations (and sometimes higher-degree polynomials) by expressing the equation as a product of simpler binomials or polynomials. Let's look at how to solve a quadratic equation by factoring.

### Example:
Solve the equation:

\[
x^2 - 5x + 6 = 0
\]

### Step-by-Step Solution:

1. **Write the equation in standard form**: Make sure the quadratic equation is in the form \(ax^2 + bx + c = 0\).
   \[
   x^2 - 5x + 6 = 0
   \]
   This equation is already in standard form.

2. **Find two numbers that multiply to give \(c\) and add up to \(b\)**: Here, we need two numbers that multiply to 6 (the constant term) and add up to -5 (the coefficient of \(x\)).

   The two numbers are -2 and -3 because:
   \[
   -2 \times -3 = 6 \quad \text{and} \quad -2 + (-3) = -5
   \]

3. **Factor the quadratic**: Rewrite the middle term using the two numbers you found:
   \[
   x^2 - 2x - 3x + 6 = 0
   \]
   Now factor by grouping:
   \[
   (x - 2)(x - 3) = 0
   \]

4. **Solve for \(x\)**: Set each factor equal to 0 and solve for \(x\):
   \[
   x - 2 = 0 \quad \Rightarrow \quad x = 2
   \]
   \[
   x - 3 = 0 \quad \Rightarrow \quad x = 3
   \]

Thus, the solutions are:
\[
x = 2 \quad \text{or} \quad x = 3
\]

---

Would you like more examples or additional details?

Here are some related questions:
1. How do you factor when the quadratic coefficient \(a \neq 1\)?
2. What if the quadratic doesn't factor easily? How would you solve it?
3. Can you solve a cubic equation by factoring?
4. How do you solve a quadratic equation using the quadratic formula?
5. What is the difference between completing the square and factoring?

**Tip**: Always double-check your factors by multiplying them back out to ensure they give the original quadratic!

Learn how to solve the quadratic equation x^2 - 5x + 6 using factoring. This step-by-step guide covers key algebra concepts such as the quadratic equation formula, factoring technique, and the Zero Product Property. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation