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3.5: Dividing Polynomials
https://math.libretexts.org/Courses/Quinebaug_Valley_Community_College/MAT186%3A_Pre-calculus_-_Walsh/03%3A_Polynomial_and_Rational_Functions/3.05%3A_Dividing_Polynomials
We are familiar with the long division algorithm for ordinary arithmetic. We begin by dividing into the digits of the dividend that have the greatest place value. We divide, multiply, subtract, includ...We are familiar with the long division algorithm for ordinary arithmetic. We begin by dividing into the digits of the dividend that have the greatest place value. We divide, multiply, subtract, include the digit in the next place value position,. Division of polynomials that contain more than one term has similarities to long division of whole numbers. We can write a polynomial dividend as the product of the divisor and the quotient added to the remainder.
5.4: Dividing Polynomials
https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_1350%3A_Precalculus_Part_I/05%3A_Polynomial_and_Rational_Functions/5.04%3A_Dividing_Polynomials
We are familiar with the long division algorithm for ordinary arithmetic. We begin by dividing into the digits of the dividend that have the greatest place value. We divide, multiply, subtract, includ...We are familiar with the long division algorithm for ordinary arithmetic. We begin by dividing into the digits of the dividend that have the greatest place value. We divide, multiply, subtract, include the digit in the next place value position,. Division of polynomials that contain more than one term has similarities to long division of whole numbers. We can write a polynomial dividend as the product of the divisor and the quotient added to the remainder.
5.5: Dividing Polynomials
https://math.libretexts.org/Bookshelves/Algebra/College_Algebra_1e_(OpenStax)/05%3A_Polynomial_and_Rational_Functions/505%3A_Dividing_Polynomials
We are familiar with the long division algorithm for ordinary arithmetic. We begin by dividing into the digits of the dividend that have the greatest place value. We divide, multiply, subtract, includ...We are familiar with the long division algorithm for ordinary arithmetic. We begin by dividing into the digits of the dividend that have the greatest place value. We divide, multiply, subtract, include the digit in the next place value position,. Division of polynomials that contain more than one term has similarities to long division of whole numbers. We can write a polynomial dividend as the product of the divisor and the quotient added to the remainder.
1.3: Divisibility and the Division Algorithm
https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Yet_Another_Introductory_Number_Theory_Textbook_-_Cryptology_Emphasis_(Poritz)/01%3A_Well-Ordering_and_Division/1.03%3A_Divisibility_and_the_Division_Algorithm
We now discuss the concept of divisibility and its properties.
2.5: Dividing Polynomials
https://math.libretexts.org/Courses/Cosumnes_River_College/Math_372%3A_College_Algebra_for_Calculus_(2e)/02%3A_Polynomial_and_Rational_Functions/2.05%3A_Dividing_Polynomials
This section covers methods for dividing polynomials, including long division and synthetic division. It explains how to use these techniques to divide a polynomial by a linear or higher-degree polyno...This section covers methods for dividing polynomials, including long division and synthetic division. It explains how to use these techniques to divide a polynomial by a linear or higher-degree polynomial, interpret the results, and find remainders. Examples illustrate each method step-by-step, helping to solve polynomial division problems efficiently.
1.5: The Division Algorithm
https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Elementary_Number_Theory_(Barrus_and_Clark)/01%3A_Chapters/1.05%3A_The_Division_Algorithm
The goal of this chapter is to introduce and prove the following important result.
3.5: Dividing Polynomials
https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_1e_(OpenStax)/03%3A_Polynomial_and_Rational_Functions/3.05%3A_Dividing_Polynomials
We are familiar with the long division algorithm for ordinary arithmetic. We begin by dividing into the digits of the dividend that have the greatest place value. We divide, multiply, subtract, includ...We are familiar with the long division algorithm for ordinary arithmetic. We begin by dividing into the digits of the dividend that have the greatest place value. We divide, multiply, subtract, include the digit in the next place value position,. Division of polynomials that contain more than one term has similarities to long division of whole numbers. We can write a polynomial dividend as the product of the divisor and the quotient added to the remainder.
3.5: Dividing Polynomials
https://math.libretexts.org/Courses/Borough_of_Manhattan_Community_College/MAT_206_Precalculus/3%3A_Polynomial_and_Rational_Functions_New/3.5%3A_Dividing_Polynomials
We are familiar with the long division algorithm for ordinary arithmetic. We begin by dividing into the digits of the dividend that have the greatest place value. We divide, multiply, subtract, includ...We are familiar with the long division algorithm for ordinary arithmetic. We begin by dividing into the digits of the dividend that have the greatest place value. We divide, multiply, subtract, include the digit in the next place value position,. Division of polynomials that contain more than one term has similarities to long division of whole numbers. We can write a polynomial dividend as the product of the divisor and the quotient added to the remainder.
1.4.4: Polynomial Division
https://math.libretexts.org/Courses/Coastline_College/Math_C097%3A_Support_for_Precalculus_Corequisite%3A_MATH_C170/1.04%3A_Polynomial_and_Rational_Functions/1.4.04%3A_Polynomial_Division
Furthermore, the coefficients of the quotient polynomial match the coefficients of the first three terms in the last row, so we now take the plunge and write only the coefficients of the terms to get ...Furthermore, the coefficients of the quotient polynomial match the coefficients of the first three terms in the last row, so we now take the plunge and write only the coefficients of the terms to get To divide $x^{3} +4x^{2} -5x-14$ by $x-2$ , we write 2 in the place of the divisor and the coefficients of $x^{3} +4x^{2} -5x-14$ in for the dividend.
3.5: The Division Algorithm and Congruence
https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book%3A_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/03%3A_Constructing_and_Writing_Proofs_in_Mathematics/3.05%3A_The_Division_Algorithm_and_Congruence
Recall that if $a$ and $b$ are integers, then we say that $a$ is congruent to $b$ modulo $n$ provided that $n$ divides $a - b$ , and we write $a \equiv b$ (mod $n$ ). (See Section 3.1....Recall that if $a$ and $b$ are integers, then we say that $a$ is congruent to $b$ modulo $n$ provided that $n$ divides $a - b$ , and we write $a \equiv b$ (mod $n$ ). (See Section 3.1.) We are now going to prove some properties of congruence that are direct consequences of the definition.
4.5: Dividing Polynomials
https://math.libretexts.org/Courses/Mission_College/Math_1%3A_College_Algebra_(Carr)/04%3A_Polynomial_and_Rational_Functions/4.05%3A_Dividing_Polynomials
We are familiar with the long division algorithm for ordinary arithmetic. We begin by dividing into the digits of the dividend that have the greatest place value. We divide, multiply, subtract, includ...We are familiar with the long division algorithm for ordinary arithmetic. We begin by dividing into the digits of the dividend that have the greatest place value. We divide, multiply, subtract, include the digit in the next place value position,. Division of polynomials that contain more than one term has similarities to long division of whole numbers. We can write a polynomial dividend as the product of the divisor and the quotient added to the remainder.

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