Fundamental theorem of algebra

Lessons

1. Introduction to Fundamental Theorem of Algebra
   For each polynomial, state the:
   • degree of the polynomial
   • nature of the roots
   • number of roots
   i) $x^3 - 2x^2 - 13x - 10$
   ii) $x^3 - 3x^2 - 9x - 5$
   iii) $x^3 - 6x^2 + 8x -15$
   iv) $x^5 - x^4 + x^3 -19x^2 +15x-63$
2. Discuss the Possible Combinations of Roots
   State the possible combinations of roots for each polynomial:
   1. $P(x) = a_7x^7 + a_6x^6 + a_5x^5 + a_4x^4 + a_3x^3 + a_2x^2 + a_1x + a_0$
   2. $P(x) = x^4 + ......$