Lesson 6
Different Forms
Problem 1
\(f(x)=(x+3)(x-4)\) and \(g(x)=\frac13(x+3)(x-4)\). The graphs of each are shown here.
- Which graph represents which polynomial function? Explain how you know.
Solution
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Problem 2
For each polynomial function, rewrite the polynomial in standard form. Then state its degree and constant term.
- \(f(x)=(x+1)(x+3)(x-4)\)
- \(g(x)=3(x+1)(x+3)(x-4)\)
Solution
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Problem 3
Tyler incorrectly says that the constant term of \((x + 4)(x - 4)\) is zero.
- What is the correct constant term?
- What is Tyler’s mistake? Explain your reasoning.
Solution
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Problem 4
Which of these standard form equations is equivalent to \((x+1)(x-2)(x+4)(3x+7)\)?
\(x^4 + 10x^3 + 15x^2 - 50x - 56\)
\(x^4 + 10x^3 + 15x^2 - 50x + 56\)
\(3x^4 + 16x^3 + 3x^2 - 66x - 56\)
\(3x^4 + 16x^3 + 3x^2 - 66x + 56\)
Solution
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Problem 5
Select all polynomial expressions that are equivalent to \(5x^3 +7x - 4x^2 + 5\).
\(13x^{5}\)
\(5x^3 - 4x^2 + 7x + 5\)
\(5x^3 + 4x \boldcdot 2 + 7x + 5\)
\(5 + 4x - 7x^2 + 5x^3\)
\(5 + 7x - 4x^2 + 5x^3\)
Solution
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(From Unit 2, Lesson 2.)Problem 6
Select all the points which are relative minimums of this graph of a polynomial function.
Point \(A\)
Point \(B\)
Point \(C\)
Point \(D\)
Point \(E\)
Point \(F\)
Point \(G\)
Solution
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(From Unit 2, Lesson 3.)Problem 7
What are the \(x\)-intercepts of the graph of \(y=(3x+8)(5x-3)(x-1)\)?
Solution
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(From Unit 2, Lesson 5.)