Factor a Polynomial Using Rational Root and Factor Theorems
Factor cubic polynomials using the Rational Root Theorem and Factor Theorem. Generate random polynomials, test possible rational roots, and see complete step-by-step factorization.
📐 Polynomial Factorer
Factor cubic polynomials using Rational Root Theorem
📖 Rational Root Theorem: If polynomial \( P(x) = a_n x^n + ... + a_0 \) has rational zeros \( \frac{p}{q} \), then \( p \) divides the constant term and \( q \) divides the leading coefficient. 📖 Factor Theorem: \( x - r \) is a factor iff \( P(r) = 0 \).
\( P(x) = x^3 - 6x^2 + 11x - 6 \)
Factor the cubic polynomial completely. Click "Show me" for each step.
📖 Step-by-Step Solution
STEP 1: Factor out the leading coefficient (if possible)
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STEP 2: List all possible rational roots and test using Factor Theorem
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STEP 3: Divide polynomial by the found factor and factor completely