Algebra 2

Polynomial expressions, equations, & functions

Advanced polynomial factorization

Factoring sum of cubes

a3+b3=(a+b)(a2ab+b2)a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Factoring difference of cubes

a3b3=(ab)(a2+ab+b2)a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Logarithms

  • x0 = 1 (as long as x ≠ 0)
  • e = lim x → ∞ (1 + (1 / x))x ≈ 2.72
  • logb = y ⇔ by = x

Logarithms:

  • log10(x) = log(x) (common log)
  • loge(x) = ln(x) (natural log)

Logarithm properties:

  • log(AB) = log(A) + log(B)
  • log(A/B) = log(A) - log(B)
  • log(A)k = k log(A)

Change of base formula:

  • logb(x) = log(x) / log(b) = ln(x) / ln(b)

ln(x) are ex inverse functions, meaning ln(ex) = eln(x) = x. For example:

  • eln(2) = 2
  • ln(e) = 1 ⇔ e1 = e
  • ln(1) = 0 ⇔ e0 = 1