Questions and Answers
What is the purpose of factoring out the Greatest Common Factor (GCF) in a quadratic equation?
The GCF of an expression is the smallest number that divides all the terms without leaving a remainder.
False
What is the first step in factoring out the GCF of a quadratic equation?
Write down the quadratic equation in the form of ax^2 + bx + c = 0.
The GCF of the terms 6x^2, 12x, and 18 is ___________.
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Match the following steps with their descriptions:
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What is the factored form of the equation 4x^2 + 12x + 8 = 0?
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Factoring out the GCF is only applicable to quadratic equations with three terms.
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What is the benefit of factoring out the GCF in a quadratic equation?
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Study Notes
Factoring Out Greatest Common Factor (GCF)
Factoring out the Greatest Common Factor (GCF) is a method used to factor quadratic equations.
What is the Greatest Common Factor (GCF)?
- The GCF is the largest number that divides all the terms of an expression without leaving a remainder.
- To find the GCF, list the factors of each term and identify the common factors.
Steps to Factor Out the GCF:
- Write down the quadratic equation: Start with a quadratic equation in the form of ax^2 + bx + c = 0.
- Find the GCF of the terms: Identify the GCF of the coefficients a, b, and c.
- Factor out the GCF: Divide each term by the GCF and write the equation in the form of GCF( expression ) = 0.
- Simplify the expression: Simplify the expression inside the parentheses by combining like terms.
Example:
Factor the quadratic equation: 4x^2 + 12x + 8 = 0
- Find the GCF: The GCF of 4, 12, and 8 is 4.
- Factor out the GCF: 4(x^2 + 3x + 2) = 0
- Simplify the expression: The factored form of the equation is 4(x + 1)(x + 2) = 0.
Key Points:
- Factoring out the GCF is a useful method for factoring quadratic equations.
- The GCF is the largest number that divides all the terms of an expression without leaving a remainder.
- Factoring out the GCF can help simplify the equation and make it easier to solve.
Factoring Out Greatest Common Factor (GCF)
What is the Greatest Common Factor (GCF)?
- The GCF is the largest number that divides all the terms of an expression without leaving a remainder.
- To find the GCF, list the factors of each term and identify the common factors.
Steps to Factor Out the GCF:
- Write down the quadratic equation in the form of ax^2 + bx + c = 0.
- Identify the GCF of the coefficients a, b, and c.
- Factor out the GCF by dividing each term by the GCF and writing the equation in the form of GCF(expression) = 0.
- Simplify the expression inside the parentheses by combining like terms.
Example of Factoring Out GCF:
- Factor the quadratic equation: 4x^2 + 12x + 8 = 0.
- The GCF of 4, 12, and 8 is 4.
- Factor out the GCF: 4(x^2 + 3x + 2) = 0.
- Simplify the expression: 4(x + 1)(x + 2) = 0.
Key Points:
- Factoring out the GCF is a useful method for factoring quadratic equations.
- Factoring out the GCF can help simplify the equation and make it easier to solve.
- The GCF is the largest number that divides all the terms of an expression without leaving a remainder.
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Description
This quiz covers the method of factoring out the Greatest Common Factor (GCF) to solve quadratic equations, including how to find the GCF and the steps to factor out the GCF.
