Question

section 3.5
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question 1
find all zeros of the function f(x) = 2x³ - 8x² - 2x + 8. enter the zeros separated by commas.
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Explanation:

Step1: Factor by grouping

Group the terms: $(2x^3 - 8x^2) + (-2x + 8)$. Factor out common factors from each group: $2x^2(x - 4) - 2(x - 4)$.

Step2: Factor out the common binomial

Now, factor out $(x - 4)$: $(2x^2 - 2)(x - 4)$.

Step3: Factor the quadratic

Factor $2x^2 - 2$: $2(x^2 - 1) = 2(x - 1)(x + 1)$.

Step4: Set each factor to zero

Set $x - 4 = 0$, $x - 1 = 0$, and $x + 1 = 0$. Solving these gives $x = 4$, $x = 1$, $x = -1$.

Answer:

-1, 1, 4