**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.

Examples

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**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) $x^5 - x^4 + x^3 -19x^2 +15x-63$**Discuss the Possible Combinations of Roots**

State the possible combinations of roots for each polynomial: