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Precalculus · A-APR

Polynomial Theorems — Rational Root and Fundamental Theorem

Rational Root Theorem — possible rational roots of aₙxⁿ+…+a₀ are ±(factors of a₀)/(factors of aₙ). Test each with synthetic division.

PrecalculusCommon Core HSA-APR.B.3A-APRVerified correct ✓

Worked examples

Let f(x) = x³ + (1)x² + (1)x + (1). Use the Factor Theorem: evaluate f(-1). Is x − (-1) a factor? (If f(-1) = 0, yes.)
Answer: 0

A polynomial has leading coefficient 4 and constant term 4. By the Rational Root Theorem, how many distinct possible rational roots are there? (List ±factors of constant term / ±factors of leading coefficient.)
Answer: 10

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Solve Higher-Degree Polynomial Equations Remainder and Factor Theorem

Polynomial Theorems — Rational Root and Fundamental Theorem

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