Fundamental theorem of algebra

All in One Place

Everything you need for better grades in university, high school and elementary.

Learn with Ease

Made in Canada with help for all provincial curriculums, so you can study in confidence.

Instant and Unlimited Help

Get the best tips, walkthroughs, and practice questions.

  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.