Is x-1 a factor of 2*x^4+3*x^2-5x+7?
Relevant Theorem: Factor's Theorem, also known as the Factor Theorem, is a fundamental result in algebra that establishes a relationship between the factors of a polynomial and its roots. It states that if a polynomial f(x) has a root r, then (x-r) is a factor of the polynomial, and conversely, if (x-r) is a factor of the polynomial, then r is a root of the polynomial.

Mathematically, the Factor Theorem can be expressed as follows:

If f(r) = 0 for some value r, then (x-r) is a factor of f(x).

And conversely,

If (x-r) is a factor of f(x), then f(r) = 0.

The Factor Theorem is a special case of the Remainder Theorem, which states that when a polynomial f(x) is divided by (x-r), the remainder is f(r). If f(r) = 0, then the remainder is zero, and (x-r) is a factor of f(x).

The Factor Theorem is useful for finding the factors of a polynomial and solving polynomial equations. By identifying the roots of a polynomial, we can determine its factors and vice versa. This theorem is particularly helpful when dealing with polynomials of higher degrees, as it simplifies the process of finding factors and roots.
False