Final answer:
Betty uses synthetic division, which is a method that involves using the coefficients of the polynomial and the constant of the divisor to efficiently obtain the quotient and remainder, but none of the provided options accurately describe this process.
Step-by-step explanation:
When Betty is dividing 4x^4 - 2x + 3 by x+2 using synthetic division, she is not specifically using any one method listed in the options provided. Synthetic division is a shortcut method of polynomial division, particularly when dividing by a linear expression, and it simplifies the process substantially.
In synthetic division, you use only the coefficients of the polynomial and the constant term from the linear divisor (x + a), using a as the divisor in synthetic division. The process involves bringing down the leading coefficient, multiplying it by the divisor, and adding it to the next coefficient, and so on, until you reach the final remainder.
None of the provided choices A) dividing the leading term of the dividend by the divisor, B) dividing each term of the dividend by the divisor, C) applying the Remainder Theorem, or D) finding the quotient and remainder by long division precisely describes the synthetic division process.
Synthetic division is more related to the concept of the Remainder Theorem, but it's not 'applying' it in the sense meant by the option C and it is certainly a different process than long division described in option D.