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HW Fundamental Theorem of Algebra

Identify the number of solutions or zeros.

1. f(x) = 5x3 - 6x2 + 2x ( 3 2. g(s) = 8s6 ( 3s4 ( 11s3 ( 2s2 + 4

3. (3y7 + 5y5( 12y + 2 = 6 4. 4 ( 7x = x2 - 3x5

Find all the zeros of the polynomial function.

5. h(x) = x3 ( 3x2 ( x + 3 6. f(x) = x4 ( 4x3 ( 20x2 + 48x

7. g(x) = x3 + 5x2 + x + 5 8. g(x) = x4 ( 9x3 + 23x2 ( 81x + 126

9. f(x) = x3 ( x2 ( 1 lx + 3 10. h(x) = 2x4 + x3 + x2 + x ( 1

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.

5. 11. (7,(4 12. 4, i, (I 13. 8,2 + i

Use a graphing calculator to graph the function. Then use the zero (or g root) feature to approximate the real zeros of the function.

18. 14. g(x) = x3 - x2 ( 5x + 3 15. g(x) = x4 ( x3 x( 20x2 + 10x + 27

22. Sporting Goods For 1998 through 2005, the sales S (in billions of dollars) of sporting goods can be modeled by S = 0.007t3 + 0.1t2 + 1.4x + 70 where t is the number of years since 1998. In which year were sales about $78 billion?

23. Grocery Store Revenue For the 25 years that a grocery store has been open, its annual revenue R (in millions of dollars) can be modeled by

R = ((t4 + 12t3 77t2 + 600t + 13,650)

where t is the number of years the store has been open. In what year(s) was the revenue $1.5 million?

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