Polynomials

  1. \rhd  The Fundamental Theorem of Algebra (5:33) A discussion on the fundamental theorem of algebra relating the degree of a polynomial and the number of real and non-real roots.
  2. \rhd Quadratics and the Fundamental Theorem of Algebra (6:34) What does the Fundamental Theorem of Algebra say about the polynomial 5x^2+6x+5?  Find its roots and check its graph.
  3. \rhd  The number of possible real roots of a polynomial (3:45) How many real roots can a degree-7 polynomial have?
  4. \rhd Sketching the graph of a polynomial (23:04) Graph f(x)=x^3-3x^2-2x+6 by finding the roots of f in exact form and its complete factorization.
  5. \rhd Finding a polynomial f that fits the given data (3:50) f has degree 3, the leading coefficient is 5, and the roots of f are precisely -3, 2, 5.
  6. \rhd Finding a polynomial f that fits the given data (2:57) f has degree 3, the roots of f are precisely 1, -2, 3, and f(0)=-12.
  7. \rhd Finding a polynomial f that fits the given data (4:53) f has degree 4, and the leading coefficient is -3.  The coefficients of f are all real. The polynomial f has roots 1, 2 and 3i.