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Questions and Answers
What is the primary purpose of factoring out the Greatest Common Factor in a quadratic expression?
What is the primary purpose of factoring out the Greatest Common Factor in a quadratic expression?
What is the first step in factoring out the Greatest Common Factor of a quadratic expression?
What is the first step in factoring out the Greatest Common Factor of a quadratic expression?
What is the result of factoring out the GCF of the expression 2x^2 + 6x + 4?
What is the result of factoring out the GCF of the expression 2x^2 + 6x + 4?
What is the definition of the Greatest Common Factor (GCF) in a quadratic expression?
What is the definition of the Greatest Common Factor (GCF) in a quadratic expression?
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Why is factoring out the GCF a crucial step in solving quadratic equations and graphing quadratic functions?
Why is factoring out the GCF a crucial step in solving quadratic equations and graphing quadratic functions?
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What happens to each term of the quadratic expression when factoring out the GCF?
What happens to each term of the quadratic expression when factoring out the GCF?
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Study Notes
Factoring Out Greatest Common Factor (GCF)
What is Factoring Out GCF?
- Factoring out the Greatest Common Factor (GCF) is a method used to simplify quadratic expressions.
- It involves finding the common factor that divides all terms of the expression and rewriting the expression as a product of the GCF and the remaining factors.
How to Factor Out GCF
- Find the GCF: Identify the greatest common factor of all terms in the quadratic expression.
- Rewrite the expression: Divide each term by the GCF and rewrite the expression as a product of the GCF and the remaining factors.
Example
- Original expression: 2x^2 + 6x + 4
- Find the GCF: 2
- Divide each term by the GCF: x^2 + 3x + 2
- Rewrite the expression: 2(x^2 + 3x + 2)
Key Points
- Factoring out the GCF simplifies the quadratic expression and makes it easier to work with.
- The GCF is the largest common factor that divides all terms of the expression.
- Factoring out the GCF is a crucial step in solving quadratic equations and graphing quadratic functions.
Factoring Out Greatest Common Factor (GCF)
What is Factoring Out GCF?
- Factoring out the Greatest Common Factor (GCF) is a method used to simplify quadratic expressions by finding the common factor that divides all terms of the expression and rewriting it as a product of the GCF and the remaining factors.
How to Factor Out GCF
- Find the GCF of all terms in the quadratic expression.
- Divide each term by the GCF and rewrite the expression as a product of the GCF and the remaining factors.
Example
- Original expression: 2x^2 + 6x + 4
- Find the GCF: 2
- Divide each term by the GCF: x^2 + 3x + 2
- Rewrite the expression: 2(x^2 + 3x + 2)
Key Points
- Factoring out the GCF simplifies the quadratic expression and makes it easier to work with.
- The GCF is the largest common factor that divides all terms of the expression.
- Factoring out the GCF is a crucial step in solving quadratic equations and graphing quadratic functions.
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Description
Learn how to simplify quadratic expressions by factoring out the Greatest Common Factor (GCF). Understand the steps to identify the GCF and rewrite the expression.
