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Rational Zeros Calculator

Find possible rational zeros using the Rational Root Theorem

Polynomial Coefficients (comma-separated)

Enter coefficients from highest to lowest degree

For polynomial: aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀ = 0

If p/q is a rational zero (in lowest terms), then:

• p is a factor of the constant term (a₀)

• q is a factor of the leading coefficient (aₙ)

Leading coefficient: 2

Constant term: 6

Factors of 6 (p): ±1, ±2, ±3, ±6

Factors of 2 (q): ±1, ±2

Possible rational zeros (p/q):

±1, ±2, ±3, ±6, ±1/2, ±3/2

Test each to find actual zeros!

Algebra

• Finding polynomial roots

• Factoring polynomials

• Solving equations

Mathematics

• Number theory

• Root finding

• Polynomial analysis

Calculus

• Critical points

• Optimization

• Curve sketching

• The theorem gives POSSIBLE zeros, not guaranteed zeros

• You must test each candidate by substitution

• Once found, use synthetic division to factor

• Irrational and complex zeros won't appear in this list

• The list can be long for polynomials with many factors