Math Problem Statement
Factor the trinomial.
x2 + 4x − 12
Solution
To factor the trinomial , we need to find two numbers that multiply to (the constant term) and add to (the coefficient of the middle term).
Let's follow the steps:
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Identify the coefficients:
- (coefficient of )
- (coefficient of )
- (constant term)
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Find two numbers that multiply to and add to :
- The numbers that work are and because:
- The numbers that work are and because:
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Rewrite the middle term using these two numbers:
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Factor by grouping:
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Factor out the common binomial:
So, the factored form of the trinomial is .
Would you like more details, or do you have any questions?
Related Questions:
- How do you factor trinomials when the leading coefficient is not 1?
- What is the difference between factoring by grouping and using the quadratic formula?
- Can all quadratic trinomials be factored using integers?
- How do you factor perfect square trinomials?
- What are the applications of factoring trinomials in real-world problems?
Tip: When factoring, always check your work by expanding the factors to ensure they multiply back to the original expression.
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Math Problem Analysis
Mathematical Concepts
Algebra
Factoring
Quadratic Equations
Formulas
Factoring quadratic trinomials
Theorems
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Suitable Grade Level
Grades 7-9