Polynomials — Chapter Summary

A polynomial p(x) = aₙxⁿ +

A polynomial p(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀ where aₙ ≠ 0. Classification: Monomial (1 term like 5x³), Binomial (2 terms like x² + 3), Trinomi

To find p(a)

To find p(a), substitute x = a in the polynomial. Example: If p(x) = 2x² - 3x + 1, then p(2) = 2(2)² - 3(2) + 1 = 8 - 6 + 1 = 3. Step-by-step: Replace

A zero of polynomial p(x)

A zero of polynomial p(x) is a value 'a' such that p(a) = 0. Finding zeros: Set p(x) = 0 and solve. For linear polynomial ax + b = 0, zero is x = -b/a

Factor Theorem

Factor Theorem: (x - a) is a factor of p(x) if and only if p(a) = 0. Application steps: 1) Find potential zeros by testing factors of constant term, 2

Key identities with step

Key identities with step-by-step applications: (x + y)² = x² + 2xy + y², (x - y)² = x² - 2xy + y², (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx, (x +