Chapter 2: Polynomials Notes

Sections

1. 2A The language of polynomials Mastered

   Polynomials, leading term, leading coefficient, degree, monic and constant term; adding, subtracting and multiplying polynomials; identically equal polynomials; polynomial equations.

   Open notes
2. 2B Graphs of polynomial functions Mastered

   Sketch polynomials from their factored form using the leading term, the zeroes and the sign, and how the graph behaves at simple and multiple zeroes.

   Open notes
3. 2C Division of polynomials Mastered

   Polynomial long division, the division theorem P(x) = A(x)Q(x) + R(x) with deg R less than deg A, and how it compares with dividing whole numbers.

   Open notes
4. 2D The remainder and factor theorems Mastered

   The remainder theorem and the factor theorem with proofs, finding integer zeroes from factors of the constant term, and factoring a polynomial fully.

   Open notes
5. 2E Consequences of the factor theorem Mastered

   Factoring after finding several zeroes, the bound of n zeroes for a degree n polynomial, the test for identical polynomials, and multiple roots as tangents when finding intersections.

   Open notes
6. 2F Sums and products of zeroes Mastered

   Formulae for the sum and product of zeroes of quadratics, cubics and quartics, the general pattern, and forming identities such as the sum of squares of the zeroes.

   Open notes
7. 2G Geometry using polynomial techniques Mastered

   Use sums and products of roots to find midpoints of chords, chord lengths and conditions for tangency when a line meets a parabola.

   Open notes