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Name:__________ warm-up 5-8

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1 Name:__________ warm-up 5-8
Solve x2 + 4x + 7 = 0 How many negative real zeros does p(x) = x4 – 7x3 + 2x2 – 6x – 2 have? A B. 2 C D. 0 What best describes the roots of the equation 2x3 + 5x2 – 23x + 10 = 0? . 3 imaginary B. 2 imaginary C. 3 real D. 2 real What is the least degree of a polynomial function with zeros that include 5 and 3i? A B. 3 C D. 1

2 Which of the following is not a zero of 4x3 + 9x2 + 22x + 5?
B. C. –1 + 2i D. –1 – 2i

3 5-8 Rational Zero Theorem
x 6 – 35x = 0. x 4 – 29x = 0. x 4 – 29x = 0

4 Details of the Day Activities: EQ:
How do polynomials functions model real world problems and their solutions? I will be able to… Identify possible rational zeros of a polynomial function Activities: Warm-up Review homework Notes: Marking Period Exam – November 13 All make-up work due Wednesday, -no Nov 4 exceptions Vocabulary: . Find all of the rational zeros of a polynomial function

5 A Quick Review Solve x2 + 4x + 7 = 0
How many negative real zeros does p(x) = x4 – 7x3 + 2x2 – 6x – 2 have? A B. 2 C D. 0 What best describes the roots of the equation 2x3 + 5x2 – 23x + 10 = 0? . 3 imaginary B. 2 imaginary C. 3 real D. 2 real What is the least degree of a polynomial function with zeros that include 5 and 3i? A B. 3 C D. 1

6 A Quick Review Which of the following is not a zero of 4x3 + 9x2 + 22x + 5? A. B. C. –1 + 2i D. –1 – 2i

7 Notes and examples

8 Notes and examples List all of the possible rational zeros of f(x) = 3x4 – x3 + 4.

9 Notes and examples List all of the possible rational zeros of f(x) = x4 + 7x3 – 15.

10 Notes and examples List all of the possible rational zeros of f(x) = x3 + 3x + 24. A. B. C. D.

11 Notes and examples GEOMETRY The volume of a rectangular solid is 1120 cubic feet. The width is 2 feet less than the height, and the length is 4 feet more than the height. Find the dimensions of the solid. Write the equation for volume The leading coefficient is 1, so the possible integer zeros are factors of Since length can only be positive, we only need to check positive zeros The leading coefficient is 1, so the possible integer zeros are factors of Since length can only be positive, we only need to check positive zeros.

12 Notes and examples ℓ = 14 ft, w = 8 ft, and h = 10 ft

13 Notes and examples

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