Algebraic For the following exercises, find the x- or t-intercepts of the polynomial functions. 6. C (t) = 2(t - 4) (t + 1) (t - 6) 7. C (t) = 3 (t + 2) (t - 3) (t +5) 8. C (t) = 4t(t - 2)2(t + 1) 9. C (t) = 2t (t - 3) (t + 1) 2 10. C (t) = 2t4 - 8+3 + 6+2 11. C (t) = 4t4 + 12+3 - 40+2 12. f (x) = x4 - x2 13. f(x) = x3 + x2 - 20x 14. f(x) = x3 + 6x2 - 7x 15. f(x) = x3 + x2 - 4x - 4 16. f(x) = x3 + 2x2 - 9x - 18 17. f(x) = 2x3 - x2 - 8x + 4 18. f(x) = x6 - 7x3 - 8 19. f (x) = 2x4 + 6x2 - 8 20. f (x) = x3 - 3x2 - x + 3 21. f (x) = x6 - 2x4 - 3x2 22. f (x) = x6 - 3x4 - 4x2 23. f (x) = x5 - 5x3 + 4xFor the following exercises, use the Intermediate Value Theorem to confirm that the given polynomial has at least one zero within the given interval. 24. f(x} = x3 - 93:, between 3: = -4 and x = -2. g. f(x} = x3 - 93:, between 3: = 2 and x = 4. 26. f(x} = x5 - 2x, between 3: = land x = 2. .f(x} = -x4+ 4,between x = land x = 3. 23. f(x} = -2x3 - x, between 3: =-1 and x = 1. @. f(x} = x3 - 100x 4- 2, between x = 0.01 and x = 0.1 For the following exercises, find the zeros and give the multiplicity of each. 30. f(x} = (x + 2)3(x - 3)2 a. f(x} = x2(2x + 3%: - 4}2 32. f(x} = x3(x-1)3(x + 2) @400 = x2 (x2 +4x+ 4) 34. f(x} = (2x +1)3 (9)::2 6x +1) g. f(x} = (3x + 2)5 (x2 - 10x + 25) 36. f(x} = x (43:2 - 12x + 9) (x2 + 8x +16) a. f(x} = x6 - x5 - 2x4 33. f(x} = 3x4 + 6x3 + 33:2 @. f(x} = 4x5 - 12x4 + 9x3 40. f(x} = 2x4 (x3 - 4x2 + 4x) . f(x} = 4x4 (9x4 -12.1i:3 + 4x2) For the following exercises, use the graphs to write the formula for a polynomial function of least degree. 48. x} For the following exerciges, use the graph to identify zeros and multiplicity. g. y 51 For the following exercises, use the given information about the polynomial graph to write the equation. . Degree 3. Zeros at x = -2, x = 1, and x = 3.}r-intercept at (U, - 4). 58. Degree 3. Zeros at x = -5, x = -2, and x = 1. yintercept at (0, 6) Q. Degree 5. Roots of multiplicity 2 at x = 3 and x = 1 , and a root of multiplicity 1 at x = -3. y-intercept at (0. 9) 60. Degree 4. Root of multiplicity 2 at x = 4, and a roots of multiplicity 1 at x = 1 and x = -2. y-intercept at (0. -3). 6_1. Degree 5. Double zero at x = 1, and triple zero at x = 3. Passes through the point (2,15). 62. Degree 3. Zeros at x = 4, x = 3, and x = 2.yintercept at (0,-24}. Q. Degree 3. Zeros at x = -3, x = -2 and x = 1.yinterceptat(0,12). 64. Degree 5. Roots of multiplicity2 at x : -3 and x = 2 and a root of multiplicity1 atx = -2. y-intercept at (0, 4) . 6_5. Degree 4. Roots of multiplicity2 at x ' % and roots of multiplicity 1 at x = 6 and x = -2. y-intercept at (0,18) . 66. Double zero at x = -3 and triple zero at x = 0. Passes through the point (I, 32)