\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)

Real Polynomials

Learning tasks
                  
Lesson Summary
Text book
Exercises Correction
A) Definitions
    1) Identifying Polynomial PropertiesEx 1 Ex 2 Ex 3
    2) Classifying Polynomials by DegreeEx 4 Ex 5 Ex 6 Ex 7 Ex 8
    3) Identifying CoefficientsEx 9 Ex 10 Ex 11
B) Operations with Polynomials
    4) Performing Linear OperationsEx 12 Ex 13 Ex 14 Ex 15
    5) Expanding PolynomialsEx 16 Ex 17 Ex 18 Ex 19
    6) Identifying CoefficientsEx 20 Ex 21 Ex 22 Ex 23
C) The Division Algorithm
    7) Performing Polynomial DivisionEx 24 Ex 25 Ex 26 Ex 27
    8) Verifying DivisibilityEx 28 Ex 29 Ex 30
    9) Finding Coefficients of FactorsEx 31 Ex 32 Ex 33
D) The Remainder and Factor Theorems
    10) Applying the Remainder TheoremEx 34 Ex 35 Ex 36
    11) Verifying DivisibilityEx 37 Ex 38 Ex 39
    12) Finding Unknown CoefficientsEx 40 Ex 41 Ex 42
    13) Factorising Polynomials Given a FactorEx 43 Ex 44
E) Quadratic Equations with Complex Roots
    14) Solving Quadratic EquationsEx 45 Ex 46 Ex 47 Ex 48
    15) Factoring PolynomialsEx 49 Ex 50 Ex 51
F) The Fundamental Theorem of Algebra
    16) Applying the Conjugate Root TheoremEx 52 Ex 53 Ex 54
G) Sum and Product of Roots Theorem
    17) Applying Vieta's FormulasEx 55 Ex 56 Ex 57 Ex 58
    18) Finding All Roots of a PolynomialEx 59 Ex 60 Ex 61 Ex 62