Exam Strategy

Readiness Check

• Find candidate zeros from the numerator.
• Exclude values that make the denominator zero.
• State domain restrictions clearly.
• For $r\ge 0$ / $r\le 0$, use zeros of both polynomials as interval endpoints/asymptotes.

Before the Exam

1. Drill: factor num and den; list domain exclusions; keep valid numerator zeros. 2. Drill: shared factor cases—candidate eliminated from zeros of $r$. 3. Build sign charts using num zeros + den zeros. 4. Match graphs: $x$-intercepts only where $r=0$ in domain.

During Multiple Choice

• Check domain before selecting a zero.
• “$x=a$ makes both zero” is usually not a zero of $r$.
• Inequality answers need all critical values from num and den.

During Free Response

1. Factor if helpful; solve $p(x)=0$. 2. State domain: $q(x)\ne 0$. 3. List zeros of $r$ with justification “in domain.” 4. For inequalities: list critical values from both polynomials, test intervals, conclude.

Common Traps

• Listing every numerator root automatically.
• Treating denominator zeros as zeros of $r$.
• Sign chart missing a denominator zero (missed asymptote barrier).

60-Second Checklist

• Numerator candidates?
• Domain filter applied?
• Inequality: both polynomials’ real zeros marked?