Question

Factor Theorem: When a polynomial expression is divided by (x - a), if the remainder (as found using the remainder theorem) is 0, then (x - a) is a factor of the original polynomial.

A. True
B. False

Answer 1

The statement that (x - a) is a factor of the polynomial expression if the remainder is 0 when divided by (x - a) is true according to the Factor Theorem. This theorem is a fundamental concept in algebra that connects roots of a polynomial with its factors.

Step-by-step explanation:

The statement given is: Factor Theorem: When a polynomial expression is divided by (x - a), if the remainder (as found using the remainder theorem) is 0, then (x - a) is a factor of the original polynomial. This statement is True.

According to the Factor Theorem, if a polynomial f(x) is divided by the binomial (x - a) and the remainder is 0, then (x - a) is indeed a factor of f(x). This means that a is a root of the polynomial, as the value of f(a) is 0. To clarify this with an example, suppose we have a polynomial f(x) and when we substitute x with a, we get f(a) = 0. This indicates that (x - a) will divide f(x) evenly, leaving no remainder.