7. s (x) = x 3 - x 2 â x + 1. 8. t (x) = x 3 + x 2 â 8x â 12. ⢠Online Homework. ⢠Hints and Help. ⢠Extra Practice. Evaluate: Homework an...
13. Manufacturing A laboratory supply company is designing a new rectangular box in which to ship glass pipes. The company has created a box with a width 2 inches shorter than its length and a height 9 inches taller than twice its length. The volume of each box must be 45 cubic inches. What are the dimensions?
Module 7
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Lesson 1
14. Engineering A natural history museum is building a pyramidal glass structure for its tree snake exhibit. Its research team has designed a pyramid with a square base and with a height that is 2 yards more than a side of its base. The volume of the pyramid must be 147 cubic yards. What are the dimensions?
15. Engineering A paper company is designing a new, pyramidshaped paperweight. Its development team has decided that to make the length of the paperweight 4 inches less than the height and the width of the paperweight 3 inches less than the height. The paperweight must have a volume of 12 cubic inches. What are the dimensions of the paperweight?
16. Match each set of roots with its polynomial function.
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3 ƒ(x)= ( x + 2)(x + 4) x – _ 2 5 3 1 x – _ x + _ 7 B. x = –2, x = –4, x = _ ƒ(x)= x – _ 4 2 2 3 5 –7 1 , x = _ ƒ(x)= ( x – 2)(x – 3)(x – 4) C. x = _ , x = _ 4 3 2 –4 , x = _ 4 x – _ 6 (x – 4) D. x = _ 6 , x = 4 ƒ(x)= x + _ 7 5 7 5 A. x = 2, x = 3, x = 4
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17. Identify the zeros of ƒ(x)= (x + 3)(x - 4)(x - 3), write the function in standard form, and state how the zeros are related to the standard form.
H.O.T. Focus on Higher Order Thinking
18. Critical Thinking Consider the polynomial function g(x)= 2x 3 - 6x 2 + πx + 5. Is it possible to use the Rational Zero Theorem and synthetic division to factor this polynomial? Explain.
19. Explain the Error Sabrina was told to find the zeros of the polynomial function h(x)= x(x - 4)(x + 2). She stated that the zeros of this polynomial are x = 0, x = -4, and x = 2. Explain her error.
c is a rational zero of a polynomial function p(x), explain why 20. Justify Reasoning If _ b bx - c must be a factor of the polynomial.
21. Justify Reasoning A polynomial function p(x)has degree 3, and its zeros are –3, 4, and 6. What do you think is the equation of p(x)? Do you think there could be more than one possibility? Explain.
