Question bank: Equivalent Expressions

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Question 1:

Medium

Consider the algebraic expression x² - 5x + 6. a) Completely factorize this expression. b) Find the roots of the equation x² - 5x + 6 = 0. c) Describe step by step how you arrived at the answers for parts a) and b).
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Question 2:

Easy

Consider the algebraic expression x² - 5x + 6. What is the correct factorization of this expression?
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Question 3:

Medium

Consider the algebraic expression 𝑥² + 8𝑥 + 15. 1. Explain step by step how to factorize this expression. 2. Then, solve the equation 𝑥² + 8𝑥 + 15 = 0 using the found factorization. 3. Finally, interpret the meaning of the obtained roots in relation to the problem that this equation can represent.
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Question 4:

Easy

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Question 5:

Medium

An engineer is solving a mathematical problem related to the structure of a building and comes across the algebraic expression (a² - b²). In order to simplify the calculation, he intends to factorize this expression using the difference of squares factorization. Which of the alternatives below presents the correctly factorized expression?
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