1. The Fundamental Theorem of Algebra Intro - Chapter 4.6

2. If every zero is counted as many times as its ______________ then, a polynomial of degree n has __________ n complex zeros. The Fundamental Theorem of Algebra Every non-constant polynomial has a ______ in the complex number system. ZERO AT MOST Every polynomial of degree n > 0 has __________ n different _______ in the complex number system. ZEROS MULTIPLICITY EXACTLY

3. Example 6: Find a polynomial of degree 3 such that 1, and – 2 are zeros, 1 has a multiplicity of 2 and

4. Conjugate Zero Theorem Let be a polynomial with ______ coefficients. If the complex number z is a zero of,then its _____________, ____, is also a zero of. Example 7: Find a polynomial with real coefficients whose zeros include the numbers 2 and 3+ i CONJUGATE REAL

5. Example 8: Factor Real plane: Complex plane: