How to factor two variables?
Understand the Problem
The question is asking how to factor expressions that involve two variables. This typically involves finding a common factor or using techniques such as grouping or applying the distributive property to rewrite the expression in a simpler form.
Answer
The factored form of the expression $x^2 + 5x + 6$ is $(x + 2)(x + 3)$.
Answer for screen readers
The factored form of the expression $x^2 + 5x + 6$ is $(x + 2)(x + 3)$.
Steps to Solve
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Identify the expression Determine the expression you need to factor. For example, consider the expression $x^2 + 5x + 6$.
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Look for common factors Inspect the expression for any common factors among all terms. In this case, there are no common factors.
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Finding two numbers Find two numbers that multiply to the constant term (here, 6) and add up to the coefficient of the linear term (here, 5). The numbers are 2 and 3 since $2 \cdot 3 = 6$ and $2 + 3 = 5$.
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Write the factors Using the two numbers, you can write the expression in its factored form. Thus, we can express $x^2 + 5x + 6$ as $(x + 2)(x + 3)$.
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Verification To ensure the factorization is correct, you can expand $(x + 2)(x + 3)$ back. This gives $x^2 + 3x + 2x + 6 = x^2 + 5x + 6$, confirming the factorization is accurate.
The factored form of the expression $x^2 + 5x + 6$ is $(x + 2)(x + 3)$.
More Information
Factoring is a fundamental skill in algebra that helps simplify expressions and solve equations. Understanding how to factor polynomials is essential for working with more complex mathematical concepts.
Tips
- Confusing the signs of the numbers: Ensure you correctly account for positive and negative numbers when finding factors.
- Forgetting to check the original expression when verifying: Always expand the factors to make sure they match the original expression.
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