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- https://math.libretexts.org/Courses/Lorain_County_Community_College/Book%3A_Precalculus_Jeffy_Edits_3.75/03%3A_Polynomial_Functions/3.02%3A_The_Factor_Theorem_and_the_Remainder_TheoremSuppose we wish to find the zeros of an arbitrary polynomial. Even though we could use the 'Zero' command to find decimal approximations for these, we seek a method to find the remaining zeros exactly...Suppose we wish to find the zeros of an arbitrary polynomial. Even though we could use the 'Zero' command to find decimal approximations for these, we seek a method to find the remaining zeros exactly. The point of this section is to generalize the technique applied here. First up is a friendly reminder of what we can expect when we divide 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_PolynomialsWe 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.
- 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_PolynomialsWe 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.
- https://math.libretexts.org/Bookshelves/Algebra/College_Algebra_1e_(OpenStax)/05%3A_Polynomial_and_Rational_Functions/505%3A_Dividing_PolynomialsWe 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.
- 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_PolynomialsThis 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.
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_1e_(OpenStax)/03%3A_Polynomial_and_Rational_Functions/3.05%3A_Dividing_PolynomialsWe 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.
- https://math.libretexts.org/Bookshelves/Algebra/College_Algebra_and_Trigonometry_(Beveridge)/02%3A_Polynomial_and_Rational_Functions/207%3A_Synthetic_DivisionThe next coefficient in the answer (4) comes from the combination of the -6 and the \(+10 .\) The +10 came from multiplying the 2 in the answer by the 5 in the divisor \(x-5 .\) The next coefficient i...The next coefficient in the answer (4) comes from the combination of the -6 and the \(+10 .\) The +10 came from multiplying the 2 in the answer by the 5 in the divisor \(x-5 .\) The next coefficient in the answer will be \(-3,\) which comes from multiplying the 4 (in the answer) by the 5 (in the divisor) and combining it with the -23 in the polynomial we're dividing into:
- https://math.libretexts.org/Courses/Borough_of_Manhattan_Community_College/MAT_206_Precalculus/3%3A_Polynomial_and_Rational_Functions_New/3.5%3A_Dividing_PolynomialsWe 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.
- https://math.libretexts.org/Courses/Northeast_Wisconsin_Technical_College/College_Algebra_(NWTC)/03%3A_Polynomial_Functions/3.05%3A_Real_Zeros_of_Polynomialsn this section, we will learn how to find good candidates to test using synthetic division. In the days before graphing technology was commonplace, mathematicians discovered a lot of clever tricks for...n this section, we will learn how to find good candidates to test using synthetic division. In the days before graphing technology was commonplace, mathematicians discovered a lot of clever tricks for determining the likely locations of zeros. Technology has provided a much simpler approach to narrow down potential candidates, but it is not always sufficient by itself.
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Stitz-Zeager)/03%3A_Polynomial_Functions/3.02%3A_The_Factor_Theorem_and_the_Remainder_TheoremSuppose we wish to find the zeros of an arbitrary polynomial. Even though we could use the 'Zero' command to find decimal approximations for these, we seek a method to find the remaining zeros exactly...Suppose we wish to find the zeros of an arbitrary polynomial. Even though we could use the 'Zero' command to find decimal approximations for these, we seek a method to find the remaining zeros exactly. The point of this section is to generalize the technique applied here. First up is a friendly reminder of what we can expect when we divide polynomials.
- https://math.libretexts.org/Courses/Mission_College/Math_1%3A_College_Algebra_(Carr)/04%3A_Polynomial_and_Rational_Functions/4.05%3A_Dividing_PolynomialsWe 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.
