CPM Homework Help : A2C Problem 9-122

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

Step 1:

Divide $2x^{3} + 3x^{2} − 8x + 3 = 0$ by $x − 1$ .

$\frac{2\textit{x}^{3}+3\textit{x}^{2}-8\textit{x}+3}{\textit{x}-1}=2\textit{x}^{2}+5\textit{x}-3$

Step 2:

Now factor the equation.

$2x^{2} + 3x^{2} − 8x + 3 = 0\\\left(x − 1\right)\left(2x^{2} + 5x − 3\right) = 0$

Step 3:

Continue to factor and find the three solutions.

Answer:

$x=1, \frac{1}{2}, -3$