Math Problem Statement
4x^2-4x-48
Solution
To factor the quadratic expression , let's start by factoring out the greatest common factor (GCF) first.
Steps:
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Factor out the GCF: The GCF of the terms , , and is 4.
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Factor the quadratic expression inside the parentheses: We need to factor .
- Find two numbers that multiply to (the constant term) and add to (the coefficient of ).
- The numbers are and because and .
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Rewrite the quadratic expression:
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Group the terms:
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Factor out the GCF from each group:
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Factor out the common binomial factor:
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Include the GCF that was factored out earlier:
So, the fully factored form of is:
Would you like further details or have any questions?
Here are some related questions you might find interesting:
- How do you identify the greatest common factor in a polynomial?
- Can you always factor out a GCF before factoring the rest of the expression?
- How do you factor trinomials with different leading coefficients?
- What if the quadratic expression doesn’t have integer roots?
- How do you solve a factored quadratic equation?
- What is the significance of the constant term in factoring?
- How do you check your work after factoring a quadratic?
- How do you factor a quadratic expression when it is not easily factorable?
Tip: Always start by factoring out the greatest common factor (GCF) before attempting to factor the quadratic expression itself. This simplifies the expression and makes the factorization process easier.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Factoring
Formulas
Quadratic equation formula ax^2 + bx + c = 0
Theorems
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Suitable Grade Level
Grades 9-12