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9-12 Integrated Math 3 Unit 3 Lesson 11

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K-5 Math 6-8 Math •9-12 Math

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Integrated Math 1 Integrated Math 2 •Integrated Math 3

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Unit 1 Unit 2 •Unit 3 Unit 4 Unit 5 Unit 6 Unit 7

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 •Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16

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Unit 3, Lesson 11

Polynomial Identities (Part 1)

$Course Icon$

Integrated Math 3

Practice

Problem 1

Select all the identities:

\((x+2)^3 = x^3 + 8\)
\((x^6 + x) = (x-1)(x^5 + x^4 + x^3 + x^2 + x)\)
\((x^2 - 1)(x^4 + x^2 + 1) = x^6 - 1\)
\((x+1)^4 = x^4 + x^3 + x^2 + x + 1\)
\((x+1)(x^4 - x^3 + x^2 - x + 1) = x^5+1\)
\((x^3 - 1)(x^3 + 1) = x^6 - 1\)

Problem 2

Is \(2(x+1)^2 = (2x+2)^2\) an identity? Explain or show your reasoning.

Problem 3

Mai is solving the rational equation \(5 = \frac{2+7x}{x}\) for \(x\). What move do you think Mai would make first to solve for \(x\)? Explain your reasoning.

Problem 4

For \(x\)-values of 0 and -2, \((x^5+32) = (x+2)^5\). Does this mean the equation is an identity? Explain your reasoning.

Problem 5

ForLesson 1: Minimizing Surface Area

Clare finds an expression for \(S(r)\) that gives the surface area, in square inches, of any cylindrical can with a specific fixed volume, in terms of its radius \(r\), in centimeters. This is the graph Clare gets if she allows \(r\) to take on any value between -1.2 and 3.

What would be a more appropriate domain for Clare to use instead?
What is the approximate minimum surface area for her can?

<p>graph of y = S of r. vertical asymptote at x = 0. x intercept at about -1. function decreasing to the left of asymptote. function decreases until y = 10 and then increases to the right of asymptote.</p>

Problem 6

ForLesson 7: Solving Rational Equations

Which values of \(x\) make \(\frac{3x+1}{x}=\frac{1}{x-3}\) true?