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Name: ________________________________________ Period: ______ Date: _______ WS • 5-1 Polynomials, Linear Factors & Zeros Write each polynomial in standard form. Then classify it by degree and by number of terms. 1. x2 + 3x 4x3 2. a3(a2 + a + 1) 3. x(x + 5) 5(x + 5) 4. 6 2x3 4 + x3 Determine the end behavior of the graph of each polynomial function. 5. y = 3x4 + 6x3 x2 + 12 6. y = 50 3x3 + 5x2 7. y = 12x4 x + 3x7 1 8. y = 20 5x6 + 3x 11x3 Determine the sign of the leading coefficient and the degree of the polynomial function for each graph. 9. 10. 11. Write each polynomial in factored form. Check by multiplication. 12. 2x3 + 10x2 + 12x 13. x4 x3 6x2 14. 3x3 + 18x2 27x Find the zeros of each function. Then graph the function. 16. y = (x + 1)(x 1)(x 3) 17. y = (x + 4)2(x + 1) Write a polynomial function in standard form with the given zeros. 19. x = 1, 3, 4 20. x = 1, 1, 2 21. x = 3, 0, 0, 5 15. x3 2x2 + x 18. y = x(x 2)(x + 5) 22. x = 1, 5, 2 23. Find the zeros of each polynomial below. For each corresponding row, shade in each number that is a zero. The illustration made from shading the squares suggests the answer to the riddle below. A. P(x) = x(x2 1) B. P(x) = x(x + 2)(x + 1)(x2 + 2x 3) __________________________ ___________________________ C. P(x) = x(x + 4)(x + 3)(x + 1)(x 1) D. P(x) = x(x2 25)(x2 + 4x + 3) ___________________________ ____________________________ E. P(x) = (x2 + x 20)(x + 2)(x2 + 4x + 3) F . P(x) = (x2 9)(x2 25) _____________________________ _____________________________ G. P(x) = (x2 + 9x + 20)(x2 5x + 6)(x 5) H. P(x) = (x2 5x + 6)(x2 9x + 20) ______________________________ ______________________________ I. P(x) = x2 6x + 9 J. P(x) = (x2 4x + 4)(x2 4x + 4) ________________________________ _______________________________ K. P(x) = x(x 2x + 1)(x 2) 2 ____________________________ A –5 –4 –3 –2 –1 0 1 2 3 4 5 B 5 –5 –4 –3 –2 –1 0 1 2 3 4 C 4 5 –5 –4 –3 –2 –1 0 1 2 3 D 3 4 5 –5 –4 –3 –2 –1 0 1 2 E 2 3 4 5 –5 –4 –3 –2 –1 0 1 F 1 2 3 4 5 –5 –4 –3 –2 –1 0 G 0 1 2 3 4 5 –5 –4 –3 –2 –1 H –1 0 1 2 3 4 5 –5 –4 –3 –2 I –2 –1 0 1 2 3 4 5 –5 –4 –3 J –3 –2 –1 0 1 2 3 4 5 –5 –4 K –4 –3 –2 –1 0 1 2 3 4 5 –5 Riddle: This grows above the ground, but the solutions to the polynomials above lie beneath. And as it grows, it provides shade to those underneath. What is it?