Understand the Definition

• Roots of a function are values where the function equals zero.

Graph the Function

• Plotting the function can provide visual insights into where the roots may lie.

Check for Rational Roots

• Use the Rational Root Theorem to identify potential rational roots from the coefficients of the polynomial.

Use Synthetic Division

• Simplify the polynomial through synthetic division to test potential roots.

Apply Numerical Methods

• Use methods such as the Newton-Raphson or bisection methods for finding roots when analytical solutions are tough.

Look for Factor Patterns

• Analyze the equation for any factorizable patterns, which may reveal roots directly.

Evaluate End Behavior

• Assess the behavior of the function as ( x ) approaches positive or negative infinity to anticipate possible roots.

Use Technology

• Leverage graphing calculators or software tools to find roots accurately.

Check Multiple Roots

• Be aware that roots can be repeated. Use the derivative to examineMultiplicity.

Consider Complex Roots

• Remember that not all roots are real; some may be complex, especially in polynomial equations.

Verify Your Solutions

• Substitute found roots back into the original equation to confirm they yield zero.

Be Aware of Domain Restrictions

• Consider any restrictions on the variable that may affect the existence of roots.