CPM Homework Help : INT3 Problem 8-93

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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 $2x^{3} + 3x^{2} – 8x + 3 = 0$ ?

Hint:

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

Step 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.

Step 2:

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

Step 3:

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

Step 4:

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.

Step 5:

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

Step 6:

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

Step 7:

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.

Step 8:

Label added, top edge, right, negative 3.

Step 9:

Label added, interior bottom, right, 3.

Step 10:

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

More Steps:

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