# Fundamental theorem of algebra

### Fundamental theorem of algebra

#### Lessons

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.
• 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:
a)
$P(x) = a_7x^7 + a_6x^6 + a_5x^5 + a_4x^4 + a_3x^3 + a_2x^2 + a_1x + a_0$

b)
$P(x) = x^4 + ......$