Math Problem Statement
Factor the quadratic expression: 2x^2 - x - 6
Solution
To factor the quadratic expression , we can follow these steps:
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Identify the coefficients: For the expression , we have:
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Multiply and : Calculate .
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Find factors of -12 that add up to :
- The factors of -12 that add up to -1 are and , because .
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Rewrite the middle term: Rewrite as , so the expression becomes:
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Factor by grouping:
- Group terms:
- Factor out the common factors in each group:
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Factor out the common binomial:
- Combine the terms to get:
So, the factored form of is:
Would you like further explanation on any of the steps?
Here are five related questions to expand on this:
- How would you factor a quadratic expression with a positive constant term?
- Can you use the same method to factor a trinomial with a different leading coefficient?
- How does the factoring process change if the middle term is positive?
- What are alternative methods to factor a quadratic if it’s not easily factorable by grouping?
- How would you verify the factors are correct?
Tip: Always check your answer by expanding the factored form to ensure it matches the original expression.
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Math Problem Analysis
Mathematical Concepts
Algebra
Factoring
Quadratic Equations
Formulas
ax^2 + bx + c = 0
Factoring by grouping
Theorems
Factoring by grouping
Suitable Grade Level
Grades 8-10