Name: using synthetic division to find factors
Uploaded: 2025-11-26T05:43:56.000Z
Duration: 1 min 28 s
Channel: JoVE

합성 나눗셈은 계수만 사용하여 다항식을 나누는 단순화된 방법입니다. 제수가 x - c 형식의 선형 이항식일 때 사용되며, 여기서 c 는 실수입니다.이 프로세스는 피제의 계수를 차순으로 쓰고 선행 항과 상수 사이에 누락된 차수에 대해 0을 삽입하는 것으로 시작됩니다. 제수의 상수 c 는 나눗셈 설정의 왼쪽에 배치됩니다.첫 번째 계수는 줄 아래에 기록됩니다. 그런 다음 상수를 곱하고 결과가 다음 계수에 추가됩니다. 이 곱셈 및 덧셈 주기는 행 전체에서 계속됩니다.행의 마지막 값은 나머지를 나타내고 이전 값은 몫의 계수(피제보다 차수가 1 작은 다항식)를 형성합니다. 최종 결과는 배당금이 제수에 몫을 더한 나머지 값과 같음으로 표현할 수 있습니다.비즈니스에서 다항식은 생산 수준에 따라 이익을 모델링할 수 있습니다. 특정 수준에서 이익을 찾기 위해 다항식을 이항식 x 에서 해당 수준을 뺀 값으로 나눕니다.이 나누기에 합성 나눗셈 방법을 사용하면 해당 수준의 이익을 나타내는 나머지가 제공됩니다.

다항식의 조립제법

Synthetic Disvision of Polynomials

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&#51312;&#47549;&#51228;&#48277;&#51008; c&#44032; &#49892;&#49688;&#51064; x - c &#44852;&#51032; &#51068;&#52264;&#49885;&#51004;&#47196; ...

Education

교육

JoVE Core

Math Fundamentals

수학 기초

Unit

단위

Polynomial and Rational Functions

다항함수와 유리함수

KEY TERMS AND CONCEPTS

주요 용어 및 개념

다항식의 종합 Disvision

using synthetic division to find factors

Synthetic division is a fast way to divide a polynomial by a linear binomial of the form x - c, where c is a real number. It gives a shorter method than polynomial long division and is useful for checking values and finding factors.

The setup starts with the coefficients of the polynomial written in descending order of powers. If a term is missing, a zero must be used to keep the columns lined up. The constant c from the divisor x - c is placed to the left of the synthetic division table.

The process begins by bringing down the first coefficient unchanged. That number is then multiplied by c and added to the next coefficient. The same multiply-and-add pattern continues until every coefficient has been used.

The final row gives the quotient coefficients, except for the last number. That last number is the remainder. For example, dividing 2x^3 - 6x^2 + 2x - 4 by x - 2 gives the quotient 2x^2 - 2x - 2 and a remainder of zero.

A remainder of zero shows that x - 2 is a factor of the polynomial. This connects synthetic division to the Remainder Theorem, which says the remainder from dividing f(x) by x - c is f(c). If that remainder is zero, the Factor Theorem confirms that x - c is a factor of f(x).

Using Synthetic Division to Find Factors

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synthetic disvision of polynomials

Synthetic division is a fast way to divide a polynomial by a linear binomial of the form x - c, where c is a real number. It gives a shorter method than polynomial long division and is useful for checking values and finding factors. The setup starts with the coefficients of the polynomial written in descending order of powers. If a term is missing, a zero must be used to keep the columns lined up. The constant c from the divisor x - c is placed to the left of the synthetic division table. The...

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key terms and concepts

Learn how synthetic division divides polynomials by x - c, finds the quotient and remainder, and shows when a binomial is a factor.

Using Synthetic Division to Find Factors | JoVE K12

The JoVE Math Fundamentals collection is designed to build a deep and comprehensive understanding of essential mathematics. Covering the foundations of algebra, geometry, trigonometry, and analytic reasoning, this course establishes a strong base for future studies. The collection connects core mathematical concepts with real-world practice, equipping learners to solve complex problems, master problem-solving skills, and apply abstract ideas.

math fundamentals

Using Synthetic Division to Find Factors

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