Look at Part 1. What techniques do you have for factoring polynomials?
GCF, product-sum, and grouping.
Is there a GCF for either expression? If so, what is it?
Yes; the GCF for the first expression is
Is the second expression factorable? If so, what technique can you use?
Factor each expression completely. What are the factored forms of each?
Look at Part 2. How can you multiply the first expression?
Answers vary; students should realize that they can distribute the terms in the first set of parentheses to the terms in the second set of parentheses and add the products.
Multiply the factors in the first expression. What is the result?
What do you think would be a common mistake when subtracting the terms in the second expression?
Answers vary; students should realize that some people might just subtract the first term in the second expression but not completely distribute the negative sign.
Subtract the expressions. What is the result?
What kind of expression is
Rational expression; both the numerator and denominator are polynomials.
How can you simplify
Answers vary; encourage students to discuss factoring the numerator and denominator to see if they share any common factors.
Do the numerator and denominator share any common factors? If so, what are they?
What is the reduced form of
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