Podcast
Questions and Answers
What is the greatest common factor (GCF)?
What is the greatest common factor (GCF)?
- The largest number that divides two or more numbers without a remainder. (correct)
- The sum of all the factors of a given number.
- The product of two or more numbers.
- The smallest number that divides two or more numbers.
Prime factorization involves breaking down a number into its composite factors.
Prime factorization involves breaking down a number into its composite factors.
False (B)
What are the two main methods to find the GCF?
What are the two main methods to find the GCF?
Prime Factorization and Listing Factors
In the DOTS formula, $a^2 - b^2$ is factored into ______
In the DOTS formula, $a^2 - b^2$ is factored into ______
What is the GCF of 12 and 18?
What is the GCF of 12 and 18?
The expression $x^2 + 4$ is an example of a difference of two squares.
The expression $x^2 + 4$ is an example of a difference of two squares.
What is the factored form of $x^2 - 25$ using the DOTS method?
What is the factored form of $x^2 - 25$ using the DOTS method?
Match the following terms with their definitions:
Match the following terms with their definitions:
What is the factored form of $x^2 - 16$?
What is the factored form of $x^2 - 16$?
The expression $9x^2 - 49$ can be factored as $(3x+7)(3x-7)$.
The expression $9x^2 - 49$ can be factored as $(3x+7)(3x-7)$.
What does SDOTC stand for in the content?
What does SDOTC stand for in the content?
In the substitution method, you first solve for one ______ in one of the equations.
In the substitution method, you first solve for one ______ in one of the equations.
Which method is best used when coefficients of a variable are opposites, or easy to become opposites?
Which method is best used when coefficients of a variable are opposites, or easy to become opposites?
The goal of the elimination method it the same as the substitution method which is to eliminate a variable.
The goal of the elimination method it the same as the substitution method which is to eliminate a variable.
What is the first step when solving a system of equations using the substitution method?
What is the first step when solving a system of equations using the substitution method?
In the elimination method, you may need to multiply one or both equations by a ______ to align the coefficient of the same variable.
In the elimination method, you may need to multiply one or both equations by a ______ to align the coefficient of the same variable.
Match each equation with its correct factored form using the difference of square method:
Match each equation with its correct factored form using the difference of square method:
Given the system of equations: $x + y = 7$ and $x - y = 1$. What is the value of $x$?
Given the system of equations: $x + y = 7$ and $x - y = 1$. What is the value of $x$?
Flashcards
What is the GCF (Greatest Common Factor)?
What is the GCF (Greatest Common Factor)?
The largest number that divides two or more numbers without leaving a remainder.
What is prime factorization?
What is prime factorization?
Breaking down a number into its prime factors, which are only divisible by 1 and themselves.
What is DOTS (Difference of Two Squares)?
What is DOTS (Difference of Two Squares)?
It's the difference between two perfect squares that can be factored into two binomials.
What's a Binomial?
What's a Binomial?
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What's the DOTS formula?
What's the DOTS formula?
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How to find the GCF using Listing Factors?
How to find the GCF using Listing Factors?
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How to find the GCF using Prime Factorization?
How to find the GCF using Prime Factorization?
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How to Factor Using DOTS?
How to Factor Using DOTS?
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Difference of Squares Pattern
Difference of Squares Pattern
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Factoring Difference of Squares
Factoring Difference of Squares
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System of Equations
System of Equations
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Substitution Method
Substitution Method
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Elimination Method
Elimination Method
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Multiplying Equations for Elimination
Multiplying Equations for Elimination
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Adding Equations to Eliminate
Adding Equations to Eliminate
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Solving for Remaining Variable
Solving for Remaining Variable
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Back Substitution
Back Substitution
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Solution to a System of Equations
Solution to a System of Equations
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Study Notes
Greatest Common Factor (GCF)
- GCF is the largest number that divides two or more numbers without a remainder, used in simplifying fractions, factoring, and ratios.
- Method 1: Prime Factorization:
- Find the prime factorization of each number (breaking it down into prime factors).
- Identify common prime factors.
- Multiply the lowest powers of the common prime factors.
- Method 2: Listing Factors:
- List all factors of each number.
- Identify the greatest common factor from the common factors.
Difference of Two Squares (DOTS)
- DOTS is a factoring technique for expressions in the form 𝑎2 - 𝑏2 (difference of two perfect squares).
- Formula: 𝑎2 - 𝑏2 = (𝑎 + 𝑏)(𝑎 - 𝑏).
- How to Factor:
- Identify perfect square terms (𝑎2 and 𝑏2).
- Apply the formula (𝑎 + 𝑏)(𝑎 - 𝑏).
Solving Systems of Equations (Substitution or Elimination)
- Used to find values of variables that satisfy two equations simultaneously.
- Substitution Method:
- Solve one equation for one variable.
- Substitute into the other equation.
- Solve for the remaining variable.
- Substitute to find the other variable.
- Elimination Method:
- Multiply/divide equations to match coefficients of a variable.
- Add/subtract equations to eliminate a variable.
- Solve for the remaining variable.
- Substitute to find the other variable.
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