CPM Homework Help : A2C Problem 9-122

Now Carlos needs to solve 2x³ + 3x² − 8x + 3 = 0, but his calculator will still only create a standard graph. He sees that the graph of y = 2x³ + 3x² − 8x + 3 crosses the x-axis at x = 1. Find all three solutions to the equation. Homework Help ✎

Step 1:

Divide 2x³ + 3x² − 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.

2x² + 3x² − 8x + 3 = 0
(x − 1)(2x² + 5x − 3) = 0

Step 3:

Continue to factor and find the three solutions.

Answer:

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