Practice - Chapter 2: Factoring Basic Expressions
Practice Questions
Test your understanding with targeted questions
What is the Greatest Common Factor (GCF) of the coefficients 10 and 15?
* Answer: 5.
* Hint: What is the largest number that divides exactly into both 10 and 15?
💡 Hint: What is the largest number that divides exactly into both 10 and 15?
Is the expression $2(3x + 4)$ fully factored? Yes or No.
* Answer: Yes.
* Hint: Is there any factor other than 1 that $3x$ and $4$ share?
💡 Hint: Is there any factor other than 1 that $3x$ and $4$ share?
7 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
Which expression represents the complete factorization of $9ab + 12b$?
* Type: mcq
* Options: $3(3ab + 4b)$, $3b(3a + 4)$, $3a(3b + 4)$, $b(9a + 12)$
* Correct Answer: $3b(3a + 4)$
* Explanation: The GCF of the coefficients (9 and 12) is 3, and the GCF of the variables ($ab$ and $b$) is $b$. The overall GCF is $3b$.
* Hint: Look for both the largest number and the highest power of the variable shared by both terms.
💡 Hint: Look for both the largest number and the highest power of the variable shared by both terms.
True or False: Factoring is the inverse operation of expanding brackets.
* Type: boolean
* Options: True, False
* Correct Answer: True
* Explanation: Expanding uses the distributive property (multiplication); factoring reverses it by identifying and pulling out the common factor (division).
* Hint: Factoring returns the expression to a product form.
💡 Hint: Factoring returns the expression to a product form.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Completely factor the expression $20a^{3}b - 16a^{2}b^{2} + 4ab$.
* Solution: The GCF of 20, 16, and 4 is 4. The GCF of $a^{3}, a^{2}, a$ is $a$. The GCF of $b, b^{2}, b$ is $b$. The overall GCF is $4ab$. The fully factored expression is $4ab(5a^{2} - 4ab + 1)$.
* Hint: Remember to check all three terms for the numerical and variable GCF, and the last term's division by the GCF must result in 1.
💡 Hint: Remember to check all three terms for the numerical and variable GCF, and the last term's division by the GCF must result in 1.
Analyze the relationship between factoring and the Statement of Inquiry. Explain how factoring basic expressions helps to "analyze and communicate complex relationships within various systems."
* Solution: Factoring helps by revealing the underlying structure (Investigating Patterns - B) of an algebraic model. For instance, an expression representing a system's total cost, $5x + 10$, factors to $5(x + 2)$. This factored form communicates (Communication - C) the relationship more clearly: it shows that the total cost is simply 5 times a base quantity $(x+2)$. This simplification makes the model easier to analyze and use for prediction (Applying Mathematics - D), as required by the Statement of Inquiry.
* Hint: Factoring is about simplifying structure. How does a simpler structure make communication and analysis easier?
💡 Hint: Factoring is about simplifying structure. How does a simpler structure make communication and analysis easier?
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