Factorisation
Understand the Problem
The question is asking about factorisation, which typically involves breaking down an expression into its constituent factors. This is a common algebraic operation.
Answer
The factored form 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 to factor First, identify the algebraic expression that needs to be factored. Let's say we have the quadratic expression $x^2 + 5x + 6$.
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Set up for factoring Look for two numbers that multiply to the constant term (6) and add to the coefficient of the linear term (5). The numbers that fit are 2 and 3.
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Write the factored form Use the numbers found to write the expression in its factored form. The expression $x^2 + 5x + 6$ can be factored as:
$$(x + 2)(x + 3)$$
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Verify the factorization To ensure the factorization is correct, expand $(x + 2)(x + 3)$ to check if it returns the original expression: $$x^2 + 3x + 2x + 6 = x^2 + 5x + 6$$
The factored form of the expression $x^2 + 5x + 6$ is $(x + 2)(x + 3)$.
More Information
Factoring is a fundamental skill in algebra, particularly beneficial for solving quadratic equations, graphing, and simplifying expressions. It helps us understand the structure of mathematical relationships.
Tips
- Forgetting to check if the factorization is correct by expanding the factors.
- Misidentifying the correct numbers that multiply and add to the terms.
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