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9-12 Algebra 2 Unit 3 Lesson 9

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Unit 3, Lesson 9

Polynomial Identities (Part 2)

Algebra 2

Practice

Problem 1

Is \(a^6 + b^6 = (a^2+b^2)(a^4 - a^2b^2 + b^4)\) an identity? Explain or show your reasoning.

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Problem 2

Match each lettered expression with the number of an expression equivalent to it.

\(\frac{1}{a} + \frac{1}{a+1}\)
\(\frac{a+1}{a-1} + \frac{a+1}{a}\)
\(\frac{1}{a} + \frac{2}{a+1}\)
\(\frac{a}{a-1} - \frac{1}{a+1}\)
\(\frac{a}{a+1} + \frac{a}{a-1}\)

\(\frac{2a^2}{a^2-1}\)
\(\frac{3a+1}{a^2+a}\)
\(\frac{2a+1}{a^2+a}\)
\(\frac{2a^2+a-1}{a^2-a}\)
\(\frac{a^2+1}{a^2-1}\)

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Problem 3

Let \((x^2+5x+4)(x+2)=A(x+1)\). If this is an identity, what is a possible expression for \(A\)?

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Problem 4

ForLesson 11: Finding Intersections

What are the points of intersection between the graphs of the functions \(f(x)=(x + 6)(2x+1)\) and \(g(x)=2x+1\)?

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Problem 5

ForLesson 7: Solving Rational Equations

Identify all values of \(x\) that make the equation true.

\(\frac{x+5}{x+11}=\frac{1}{x+5}\)
\(\frac{2x-3}{x} = \frac{14}{x+5}\)

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Problem 6

ForLesson 8: Polynomial Identities (Part 1)

Match each expression in the lettered list with the number of an expression equivalent to it.

\((x - 1)(x^3+x^2+x+1)\)
\((x+6)(x-6)\)
\((x-1)^3\)
\(x^4 - 36\)
\((x+2)^3 - x^3\)

\(x^3 - 3x^2 + 3x - 1\)
\((x^2 + 6)(x^2 - 6)\)
\(x^2 - 36\)
\(2(3x^2+6x+4)\)
\(x^4-1\)

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Lesson 9 Resources

Student Materials