How to factor an expression completely?
Understand the Problem
The question is asking for the process of factoring a mathematical expression fully, which typically involves identifying common factors, grouping, or using specific factoring formulas.
Answer
The expression $x^2 - 5x + 6$ factors to $(x - 2)(x - 3)$.
Answer for screen readers
The factored form of the expression $x^2 - 5x + 6$ is $(x - 2)(x - 3)$.
Steps to Solve
- Identify the expression to be factored
First, we need to identify the expression that we will be factoring. For example, let's consider the expression $x^2 - 5x + 6$.
- Look for common factors
Check if there are any common factors in the coefficients. In this case, there are no common factors among the terms.
- Use the quadratic formula or factoring methods
We need two numbers that multiply to the constant term (6) and add up to the linear coefficient (-5). The numbers are -2 and -3.
- Write the expression in factored form
Using the numbers identified in the previous step, we can express the quadratic in its factored form: $$x^2 - 5x + 6 = (x - 2)(x - 3)$$
- Verify the factorization
To ensure the factorization is correct, multiply the factors back together: $$(x - 2)(x - 3) = x^2 - 3x - 2x + 6 = x^2 - 5x + 6$$ This confirms our factorization is accurate.
The factored form of the expression $x^2 - 5x + 6$ is $(x - 2)(x - 3)$.
More Information
Factoring is a foundational skill in algebra that simplifies expressions and helps solve equations. The process of recognizing patterns and relationships among coefficients is critical in many areas of mathematics.
Tips
- Overlooking common factors: Always check for common factors in all terms before factoring.
- Incorrectly finding pair numbers: Be careful when picking pairs that multiply and add to the desired values; wrong selections lead to incorrect factors.
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