Answer
See the explanation
Work Step by Step
a. The Fundamental Theorem of Algebra states that:
Every polynomial $P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+...+a_{1}x+a_{0}$, $(n \geq 1, a_{n} \ne 0) $ with complex coefficients has $n$ roots, or solutions, in the complex numbers. The roots can have a multiplicity greater than zero.
b. The Complete Factorization Theorem states that:
If $P(x)$ is a polynomial of degree $n \geq 1$, then there exist complex numbers
$a, c_1, c_2, . . . , c_n$ (with $a \ne 0$) such that $P(x) = a(x - c_{1})(x - c_{2}) . . . (x - c_{n})$
c. The Zeros Theorem states that:
Every polynomial of degree $n \geq 1$ has exactly $n$ zeros, provided that a zero of multiplicity $k$ is counted $k$ times.
d. The Conjugate Zeros Theorem states that:
If the polynomial $P$ has real coefficients and if $a + bi$ is a zero of $P$, then its complex conjugate $a - bi$ is also a zero of $P$.
