Fundamental theorem of algebra

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  1. Introduction to Fundamental Theorem of Algebra
    For each polynomial, state the:
    • degree of the polynomial
    • nature of the roots
    • number of roots
    i) x32x213x10x^3 - 2x^2 - 13x - 10
    ii) x33x29x5x^3 - 3x^2 - 9x - 5
    iii) x36x2+8x15x^3 - 6x^2 + 8x -15
    iv) x5x4+x319x2+15x63x^5 - x^4 + x^3 -19x^2 +15x-63
    1. Discuss the Possible Combinations of Roots
      State the possible combinations of roots for each polynomial:
      1. P(x)=a7x7+a6x6+a5x5+a4x4+a3x3+a2x2+a1x+a0P(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)=x4+...... P(x) = x^4 + ......
    Topic Notes
    Fundamental Theorem of Algebra:
    • Every polynomial can be factored into a product of linear factors and irreducible quadratic factors.
    • A degree n polynomial has exactly n roots.