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