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K. Laws Algebra II 6.7 Notes Day 1 Using the Fundamental Theorem of Algebra Goals: I will use the fundamental theorem of Algebra to determine how many solutions a polynomial should have. I will use synthetic or long division to find all solutions of a polynomial. Review: When a real number and an imaginary number are written as a sum it is called a _______________________________. Complex Conjugate Theorem If a + bi is a zero/solution of the function, then a – bi is also a zero/solution. The Fundamental Theorem of Algebra Every polynomial of degree “n” where n > 0 has at least one solution in the complex numbers. o A polynomial with the nth degree will have n solutions. o They do not have to be distinct solutions (Can be repeated) Ex 1 Find all the zeros of the polynomial (Real and Complex). 𝑔(𝑥) = 𝑥 4 + 3𝑥 3 − 8𝑥 2 − 22𝑥 − 24 Homework: