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Answer:
This method is particularly useful for finding roots of polynomials (using methods like synthetic division) and for factoring polynomials by breaking them down into simpler components.
Step-by-step explanation:
The continuous division method is a technique used in mathematics, particularly for solving polynomial equations and simplifying expressions. It involves a process of repeatedly dividing by a divisor to find factors or roots of a polynomial.
Here's a general outline of the continuous division method:
1.) Set Up the Division: Start by dividing the polynomial by a potential divisor (usually a binomial) using polynomial long division or synthetic division.
2.) Perform Division: Carry out the division process step-by-step. For polynomial long division, divide each term of the polynomial by the leading term of the divisor, multiply, and subtract to find the remainder.
3.) Repeat if Necessary: If the result of the division is a polynomial of degree higher than one, you can repeat the division process with the quotient polynomial and another divisor.
4.) Continue Until Simplified: Continue this process until you reach a polynomial that cannot be further divided by the chosen divisor or until you factor the polynomial completely.