Here’s a practice problem:

Problem

Solve for the roots of the polynomial:
$2x^3 - 3x^2 - 2x + 3 = 0$

Instructions

1. First, check for possible rational roots using the Rational Root Theorem.
2. Use synthetic or long division to factor the polynomial.
3. Solve for the roots by factoring the remaining quadratic (if applicable).

Do you need help with solving this, or would you like to attempt it first?

5 Related Questions

1. How do you apply the Rational Root Theorem to determine possible roots?
2. What is synthetic division, and how is it used to simplify polynomials?
3. How do you factor a cubic polynomial if it doesn’t have an obvious root?
4. What is the significance of multiplicity in polynomial roots?
5. How can graphing a polynomial help in identifying its roots?

Tip

When solving higher-degree polynomials, always start by factoring out common terms or using the Rational Root Theorem to test simple values like $\pm1, \pm2$.