Math Problem Statement
solve by factoring: x2 - 5x + 6 = 0
Solution
To solve the quadratic equation by factoring, we need to find two numbers that multiply to 6 (the constant term) and add up to -5 (the coefficient of the linear term, ).
Step-by-step solution:
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Identify the factors of the constant term (6): The factors of 6 are:
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Find the pair that adds to -5: The pair and multiply to give 6 and add up to -5.
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Factor the quadratic: We can rewrite the equation as: Now, group the terms: Factor each group: Factor out the common binomial :
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Solve for : Set each factor equal to zero: Solving these gives:
Final solution:
The solutions are:
Would you like a more detailed explanation of any of the steps? Here are some related questions for you:
- What would the graph of look like?
- How would you solve a quadratic equation using the quadratic formula instead of factoring?
- What happens if the equation does not factor easily?
- How do you identify when a quadratic equation is prime (cannot be factored)?
- What are the conditions for factoring quadratics with negative coefficients?
Tip: When factoring quadratics, always start by looking for a pair of numbers that multiply to the constant term and add to the coefficient of the linear term.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Factoring
Formulas
Quadratic equation ax^2 + bx + c = 0
Factoring method
Theorems
Zero Product Property
Suitable Grade Level
Grades 7-9