Question

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Answer 1

Answer:  A) 7 real zeros and 6 turning points at 0, 2, 4

Step-by-step explanation:

x⁷ - 6x⁶ + 8x⁵

The degree (largest exponent) is 7 so the maximum number of real zeros is 7.

Factor out x⁵

x⁵(x² - 6x + 8)

Factor the quadratic

x⁵(x - 2)(x - 4)

Set each factor equal to 0 and solve for x

x⁵ = 0         --> x = 0  (multiplicity of 5)

x - 2 = 0     --> x = 2

x - 4 = 0     --> x = 4