### Home > INT3 > Chapter 8 > Lesson 8.3.1 > Problem8-93

8-93.

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

If $x = 1$, then $x − 1 = 0$.
So divide $2x^{3} + 3x^{2} − 8x + 3 = 0$ by $x − 1$.

2 by 3 rectangle, labeled as follows: left edge, x, minus 1, interior top left, 2, x cubed, bottom expression: 2, x cubed, + 3, x squared, minus 8, x, + 3. An arrow points from the interior 2, x cubed to the bottom, 2, x cubed.

Label added: top edge, left, 2, x squared.

Label added: interior bottom, left, negative 2, x squared.

Label added: interior top middle, 5, x squared, with arrow, going through, interior bottom left, negative 2, x squared, ending, in the bottom expression, at 3, x squared.

Label added, top edge, middle, 5, x.

Label added, Interior bottom, middle, negative 5, x.

Label added, interior top, right, negative 3, x, with arrow, going through, interior bottom, middle, negative 5, x, ending, in the bottom expression, at negative 8, x.

Label added, top edge, right, negative 3.

Label added, interior bottom, right, 3.

Write the equation in factored form.
$\left(x − 1\right)\left(2x^{2} + 5x − 3\right) = 0$

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