What is the multiple zero and multiplicity of f(x) = x^3-8x^2+16x

x = 4 with multiplicity 2

Step-by-step explanation:

Given

f(x) = x³ - 8x² + 16x

To find the zeros equate f(x) to zero, that is

x³ - 8x² + 16x = 0 ← factor out x from each term

x(x² - 8x + 16) = 0

To factor the quadratic

Consider the factors of the constant term (+ 16) which sum to give the coefficient of the x- term (- 8)

The factors are - 4 and - 4, since

- 4 × - 4 = 16 and - 4 - 4 = - 8, hence

x² - 8x + 16) = (x - 4)(x - 4)

and

x³ - 8x² + 16x = x(x - 4)(x - 4) = 0

Equate each factor to zero and solve for x

x = 0

x- 4 = 0 ⇒ x = 4

x - 4 = 0 ⇒ x = 4

The multiple zero is x = 4 with multiplicity 2

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step-by-step explanation: