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

合成除算は、係数のみを使用して多項式を除算するための簡略化された方法です。これは、除数が x-c形式の線形二項式であり、 c は実数である場合に使用されます。このプロセスは、被除数の係数を程度の降順で書き込むことから始まり、先頭の項と定数の間に欠落している程度にはゼロを挿入します。除数からの定数 c は、除算設定の左側に配置されます。最初の係数は線の下に書かれています。次に、定数を掛け、結果を次の係数に加算します。この乗算と加算のサイクルは、行全体で継続されます。行の最後の値は余りを表し、前の値は商の係数(被除数より次数が1つ小さい多項式)を形成します。最終結果は、被除数に除数を掛けた商に余りを加えたものに等しいと表すことができます。ビジネスでは、多項式は生産レベルに基づいて利益をモデル化できます。特定のレベルでの利益を見つけるには、多項式を二項式 x からそのレベルを引いた値で割ります。この除算に合成除算法を使用すると、そのレベルでの利益を表す余りが得られます。

多項式の合成除算

Synthetic Disvision of Polynomials

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Education

JoVE Core

Math Fundamentals

数学の基礎

Unit

ユニット

Polynomial and Rational Functions

多項式関数と有理関数

KEY TERMS AND CONCEPTS

主要用語と概念

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

quadratic models

Quadratic Motion and Parabolas

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Polynomial Division: Quotient and Remainder

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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...

real zeros of polynomials

Finding Polynomial X-Intercepts

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Polynomial Roots in Complex Numbers

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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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