Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary.* ƒ(x)=x^4-6x^3+7x^2

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form of a polynomial in one variable is f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where n is a non-negative integer and a_n is not zero. Understanding the structure of polynomial functions is essential for analyzing their roots and behavior.

Complex zeros of a polynomial are the values of x for which the polynomial evaluates to zero, and they can be real or non-real (complex) numbers. According to the Fundamental Theorem of Algebra, a polynomial of degree n has exactly n roots in the complex number system, counting multiplicities. Identifying complex zeros often involves techniques such as factoring, synthetic division, or applying the quadratic formula.

Factoring is the process of breaking down a polynomial into simpler components (factors) that can be multiplied to yield the original polynomial. The Rational Root Theorem provides a method to identify possible rational roots of a polynomial, which can then be tested to find actual roots. This theorem is particularly useful for polynomials with integer coefficients, as it helps narrow down the search for zeros.