Q1. Factor: 4a + 8a

Background

Topic: Factoring by Greatest Common Factor (GCF)

This question asks you to factor an expression by finding the greatest common factor of the terms.

Key Terms and Formulas:

• Greatest Common Factor (GCF): The largest expression that divides each term of the given expression.

• Factoring: Writing an expression as a product of its GCF and another expression.

Step-by-Step Guidance

1. Identify the coefficients and variables in each term: and .

2. Find the GCF of the coefficients (4 and 8). What is the largest number that divides both?

3. Check the variables: Both terms have as a factor.

4. Factor out the GCF from both terms. Write the expression as the GCF times the remaining terms in parentheses.

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Q2. Factor: 3x - 5x

Background

Topic: Factoring by GCF

This question tests your ability to factor out the greatest common factor from two terms with the same variable.

Key Terms and Formulas:

• GCF: The largest factor common to both terms.

Step-by-Step Guidance

1. Identify the coefficients and variables: and .

2. Find the GCF of the coefficients (3 and 5). What is the largest number that divides both?

3. Both terms have as a factor.

4. Factor out the GCF and write the remaining expression in parentheses.

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Q3. Factor: 12ab - 8a2b

Background

Topic: Factoring by GCF

This problem involves factoring out the greatest common factor from terms with multiple variables and exponents.

Key Terms and Formulas:

• GCF: For coefficients and variables, take the lowest power of each variable present in all terms.

Step-by-Step Guidance

1. List the coefficients: 12 and 8. Find their GCF.

2. For variables: and . The GCF for is , and for is .

3. Combine the GCFs for coefficients and variables.

4. Factor out the GCF from each term and write the remaining expression in parentheses.

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Q4. Factor: 15cd - 10c2d

Background

Topic: Factoring by GCF

This question asks you to factor out the GCF from terms with coefficients and variables with exponents.

Key Terms and Formulas:

• GCF: Find the largest number and variable factors common to both terms.

Step-by-Step Guidance

1. Identify the coefficients: 15 and 10. Find their GCF.

2. For variables: and . The GCF for is , and for is .

3. Combine the GCFs and factor them out from both terms.

4. Write the factored expression as the GCF times the remaining terms in parentheses.

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Q5. Factor: 20fg - 15f2

Background

Topic: Factoring by GCF

This problem involves factoring out the GCF from terms with two variables, one of which has an exponent.

Key Terms and Formulas:

• GCF: The largest factor common to both terms, including variables.

Step-by-Step Guidance

1. Identify the coefficients: 20 and 15. Find their GCF.

2. For variables: and . The GCF for is .

3. Combine the GCFs and factor them out from both terms.

4. Write the expression as the GCF times the remaining terms in parentheses.

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Q6. Factor: 15y4 - 9y2

Background

Topic: Factoring by GCF

This question involves factoring out the GCF from terms with the same variable raised to different powers.

Key Terms and Formulas:

• GCF: For variables, use the lowest exponent present in all terms.

Step-by-Step Guidance

1. Identify the coefficients: 15 and 9. Find their GCF.

2. For variables: and . The GCF for is .

3. Combine the GCFs and factor them out from both terms.

4. Write the expression as the GCF times the remaining terms in parentheses.

Try solving on your own before revealing the answer!