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8-93.

Now Carlos needs to solve 2x3 + 3x2 – 8x + 3 = 0, but his calculator will still only create a graph with a standard viewing window. He sees that the graph of
y = 2x3 + 3x2 – 8x + 3 crosses the x‑axis at x = 1. What are all three solutions to 2x3 + 3x2 – 8x + 3 = 0? Homework Help ✎

If x = 1, then x − 1 = 0.
So divide 2x3 + 3x2 − 8x + 3 = 0 by x − 1.

Write the equation in factored form.
(x − 1)(2x2 + 5x − 3) = 0

Factor the quadratic expression and use the Zero Product Property to obtain the three solutions.