336 CHAPTER 3 Polynomial and Rational Functions 5. A polynomial function having degree 6 and only real coefficients may

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336 Chapter 3 Polynomial And Rational Functions 5 A Polynomial Function Having Degree 6 And Only Real Coefficients May 1 (42.74 KiB) Viewed 42 times

336 CHAPTER 3 Polynomial and Rational Functions 5. A polynomial function having degree 6 and only real coefficients may have to 6. The polynomial function f(x)=2x² + 38²-86²-5x+6 has three variation zeros. in sign. 7. M-7-6, then 2--7+61. 8. The product of a complex number and its conjugate is always a real number. Use the factor theorem and synthetic division to decide whether the second poly a factor of the first. See Example 1. 9. 2-5²+3x+1; -1 10. x+6²-2x-7; x+1 11. 2¹+5²-8²+3x+13; x+1 12. -3x²+x²5x²+2x+4; x-1 13.-+3-2; x+2 14-2+x-63; x+3 16. 5x²14x+10, x+2 15. 4x²+2x+54; x-4 17.x²+2x+3; x-1 18. 21+x+2; x+1 19. 2x+5²-2x² + 5x+6; x+3 20, 5x++ 16x²15x³ + 8x + 16; x+ Factor f(x) into linear factors given that k is a zero. See Example 2. 21. f(x)-21³-1²-17x+30 k-2 22. f(x)=2x-3x²-3x+6; k-1 23. f(x)=6x³+ 13x²-14r +3: k-3 24. f(x)-6x +17x²-63x+10; k--5 25. f(x)=6x25x² + 3x-4; 4--4 26. f(x)-850x²+47x-15; -5 27. f(x)=²+(7-3)x²+(12-21)x - 36i, k=3i 28. f(x)=2+(3+2)x² + (1+3)x+t; k=-1 29. f(x)=2x+(3-2)x+(-8-56)x+(3+3); k=1+1 30. f(x)=6x+(196)x² + (167)x+ (4-2): k=-2+1 31. f(x)=x+2-7x²-20x-12; k=-2 (multiplicity 2) f(x)=2x¹+x¹-9x²-13x-5; k=-1 (multiplicity 3) 32. For each polynomial function, one zero is given Find all other zeros. See Examples 1 and 6 33. f(x)=x²-1²-4x-6; 3 34. f(x)=x+4x²-5; 1 35. fix)=x²-7²+17x-15, 2-1 36. f(x)=41²+ 6x²-2x-1: ! 37. f(x)=x+5x²+4; -1 38. f(x)=x+26x² +25 For each polynomial function, (a) list all possible rational zeros. (b) find all rational eros, and (e) factor f(x) into linear factors. See Example 3. 39. f(x)=x-21¹-13-10 41. f(x)=x+6x²-x-30 40. f(x)=x+5x²+2x-8 42. f(x)=x²-²-10x-8