Question

Which theorem can be used to determine if a binomial is a factor of a polynomial and find the remainder?

A) Pythagorean Theorem
B) Remainder Theorem
C) Fundamental Theorem of Calculus
D) Binomial Theorem

Answer 1

The Remainder Theorem is used to determine if a binomial is a factor of a polynomial and to find the remainder by evaluating the polynomial at the value that makes the binomial zero.

Step-by-step explanation:

The theorem that can be used to determine if a binomial is a factor of a polynomial and to find the remainder is the Remainder Theorem. This theorem states that when a polynomial f(x) is divided by a binomial in the form (x - a), the remainder is the value that is obtained by substituting the value a into the polynomial, which is f(a). Conversely, the Pythagorean Theorem, the Fundamental Theorem of Calculus, and the Binomial Theorem serve different purposes in mathematics and don’t pertain to factoring polynomials and finding remainders.