Practice Objectives
- Demonstrate the ability to find the GCF for a group of monomials
- Demonstrate the ability to factor out the GCF from a polynomial
Practice Factoring Out the Greatest Common Factor (GCF)
Instructions:
Answer 7/10 questions correctly to pass.
Factor out the greatest common factor (GCF) ONLY. The expression inside of the parentheses is already provided. You will only need to enter your GCF in the blank.
- Note: Further factoring when possible is NOT required for this exercise.
- Note: When the leading coefficient is negative, factor out the -GCF
- This is typically required by most teachers for this exercise
- Factoring out either the GCF or -GCF is valid but in our case, only the -GCF will be scored correctly
- You will get an error message if you try to enter the wrong sign
- Use "^" to raise a variable to a single-digit positive integer
- Only variables can have exponents
- An exponent of zero is not allowed
- A negative exponent is not allowed
- The range of allowed coefficients is from -99 to 99 with zero being excluded
- For a common binomial factor, the parentheses will be added in when you start typing
- To make typing easier, negatives will not be factored out for common binomial factors
Problem:
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Finding the Greatest Common Factor for a Group of Monomials:
- Number Part:
- Find the prime factorization of each number
- Build a list of all prime factors that are common to ALL monomials
- Apply the appropriate exponent to each prime factor in the list
- Use the exponent that represents the least number of occurrences of the prime factor across all of the prime factorizations
- Find the product of the prime factors in the list raised to the correct exponents, this is the number part of the GCF
- If there are no prime factors in common to ALL, the GCF is 1
- Variable Part:
- Identify which variables are present in ALL monomials
- For each common variable, choose the smallest exponent of that variable that appears across all the monomials
- If there are no variables in common to ALL, the GCF is 1
- The GCF is the product of the number part and the variable part
Factoring Out the GCF:
- Place the polynomial inside of a set of parentheses
- Place the GCF outside of the parentheses
- Divide each term inside of the parentheses by the GCF
Factoring Out a Common Binomial Factor:
- Wrap the expression with brackets
- Brackets are preferred at the start to avoid confusion with parentheses
- The brackets can be swapped with parentheses at the end
- Place the common binomial factor outside of the brackets
- Remove the common binomial factor from inside of the brackets
- Combine like terms on the inside of the brackets
- Swap out the brackets for parentheses
Step-by-Step:
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