Assess Readiness
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Look at Part 1. What techniques do you have for factoring polynomials?
GCF, product-sum, and grouping.
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Is there a GCF for either expression? If so, what is it?
Yes; the GCF for the first expression is
4x . -
Is the second expression factorable? If so, what technique can you use?
Yes; product-sum.
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Factor each expression completely. What are the factored forms of each?
4x(x^2-3x-5) ;(x-9)(x+4) -
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.
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Multiply the factors in the first expression. What is the result?
8x^4-2x^2-15 -
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.
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What kind of expression is
\frac{2x^2-4x}{5x^2-10x} ? How do you know?Rational expression; both the numerator and denominator are polynomials.
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How can you simplify
\frac{2x^2-4x}{5x^2-10x} ?Answers vary; encourage students to discuss factoring the numerator and denominator to see if they share any common factors.
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Do the numerator and denominator share any common factors? If so, what are they?
Yes;
x andx-2 . -
What is the reduced form of
\frac{2x^2-4x}{5x^2-10x} ?\frac{2}{5} (x\neq 0, 2) .
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