Master solving polynomial equations using factoring, the Rational Root Theorem, synthetic division, and special factorization patterns. Learn to find all roots of higher-degree polynomials!
Find all roots of the polynomial equation!
Equation:
Practice factoring special polynomial forms!
Factor:
A polynomial equation is an equation where a polynomial is set equal to zero. The solutions (roots) are the values of x that make the equation true.
General form: aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀ = 0
Solve: x³ - 6x² + 11x - 6 = 0
Step 1: Try x = 1: 1 - 6 + 11 - 6 = 0 ✓
Step 2: Factor out (x - 1): (x - 1)(x² - 5x + 6) = 0
Step 3: Factor quadratic: (x - 1)(x - 2)(x - 3) = 0
Solution: x = 1, x = 2, or x = 3
Solve: x⁴ - 5x² + 4 = 0
Step 1: Let u = x², so u² - 5u + 4 = 0
Step 2: Factor: (u - 1)(u - 4) = 0
Step 3: Substitute back: x² = 1 or x² = 4
Solution: x = ±1, x = ±2