In Exercises 55-72, find all the zeros of the function and write the polynomial as a product of linear factors.

55. \( f(x) = x^2 + 25 \)

56. \( f(x) = x^2 - x + 56 \)

57. \( h(x) = x^2 - 4x + 1 \)

58. \( g(x) = x^2 + 10x + 23 \)

59. \( f(x) = x^4 - 81 \)

60. \( f(y) = y^4 - 625 \)

61. \( f(z) = z^2 - 2z + 2 \)

62. \( h(x) = x^3 - 3x^2 + 4x - 2 \)

63. \( g(x) = x^3 - 6x^2 + 13x - 10 \)

64. \( f(x) = x^3 - 2x^2 - 11x + 52 \)

65. \( h(x) = x^3 - x + 6 \)

66. \( h(x) = x^3 + 9x^2 + 27x + 35 \)

67. \( f(x) = 5x^3 + 9x^2 + 28x + 6 \)

68. \( g(x) = 3x^3 + 4x^2 + 8x + 8 \)

69. \( g(x) = x^4 - 4x^3 + 8x^2 - 16x + 16 \)

70. \( h(x) = x^3 + 6x^2 + 10x + 9 \)

71. \( f(x) = x^3 + 10x^2 + 9x \)

72. \( f(x) = x^4 + 29x^2 + 100 \)

To find the zeros of a polynomial function and write it as a product of linear factors, we need to set the function equal to zero and solve for x. Let's take a look at the provided exercises:

55. f(x) = x² + 2x + 1 can be factored as (x + 1)(x + 1) = 0, so the zeros are x = -1.

57. h(x) = x² - 4x + 15 can be factored as (x - 3)(x - 5) = 0, so the zeros are x = 3 and x = 5.

59. f(x) = x⁴ - 8x² + 16 can be factored as (x - 2)(x + 2)(x - 2)(x + 2) = 0, so the zeros are x = -2 and x = 2.

And so on for the rest of the exercises.

Learn more about Polynomial zeros here:

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