Exam Strategy

Readiness Check

• Connect real zero ↔ linear factor ↔ $x$-intercept.
• State multiplicity and total zeros = degree.
• Apply conjugate pairs for real coefficients.
• Predict cross vs touch from odd/even multiplicity.
• Find degree from successive differences on equal-step tables.

Before the Exam

1. Drill: given zeros (with multiplicities), write a polynomial and its degree. 2. Drill: given $a+bi$, write the conjugate and remaining real-zero possibilities by degree. 3. Graph sketches: multiplicity 1 vs 2 vs 3 at an intercept. 4. Build first/second/third differences until constant.

During Multiple Choice

• Count: multiplicities must sum to degree.
• Non-real zeros consume two slots (the pair).
• Odd degree ⇒ at least one real zero (with real coefficients).
• "Tangent to $x$-axis" ⇒ even multiplicity at that real zero.

During Free Response

1. List zeros with multiplicities. 2. Justify factors $(x-a)^m$. 3. For non-real zeros, explicitly name the conjugate. 4. If using a table, show difference rows and state the degree.

Common Traps

• Listing $a+bi$ without $a-bi$.
• Saying a degree-4 polynomial with two non-real zeros has four real intercepts.
• Mixing multiplicity (repeat factor) with "how many turning points."

60-Second Checklist

• Degree = total zeros with multiplicity?
• Conjugate written?
• Cross vs touch matches multiplicity parity?
• Equal steps before reading successive differences?