### Home > INT3 > Chapter 8 > Lesson 8.3.1 > Problem 8-93

8-93.

Now Carlos needs to solve 2*x*^{3} + 3*x*^{2} – 8*x* + 3 = 0, but his calculator will still only create a graph with a standard viewing window. He sees that the graph of

*y* = 2*x*^{3} + 3*x*^{2} – 8*x* + 3 crosses the *x*‑axis at *x *= 1. What are all three solutions to 2*x*^{3} + 3*x*^{2} – 8*x* + 3 = 0? Homework Help ✎

If *x* = 1, then *x* − 1 = 0.

So divide 2*x*^{3} + 3*x*^{2} − 8*x* + 3 = 0 by *x* − 1.

Write the equation in factored form.

(*x* − 1)(2*x*^{2} + 5*x* − 3) = 0

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