key term - Long Division

Definition

Long division is a method for dividing one polynomial by another polynomial. It involves systematically dividing the terms of the dividend by the terms of the divisor, and recording the partial quotients and remainders until the degree of the remainder is less than the degree of the divisor.

5 Must Know Facts For Your Next Test

1. Long division is a step-by-step process that can be used to divide any polynomial by another polynomial, regardless of their degrees.
2. The goal of long division is to find the quotient and remainder when dividing one polynomial by another.
3. The degree of the remainder must be less than the degree of the divisor for the division process to be complete.
4. Long division is particularly useful when the divisor is not a linear expression, as synthetic division cannot be applied in those cases.
5. The steps of long division involve repeatedly multiplying the divisor by a trial quotient, subtracting the result from the dividend, and bringing down the next term of the dividend.

Review Questions

• Explain the purpose of long division in the context of dividing polynomials.
  • The purpose of long division in the context of dividing polynomials is to find the quotient and remainder when dividing one polynomial by another. Long division is a systematic process that can be used to divide any polynomial by another polynomial, regardless of their degrees. The goal is to find the highest power of the variable in the quotient and the remainder, which must have a degree less than the degree of the divisor.
• Describe the key steps involved in the long division algorithm for dividing polynomials.
  • The key steps in the long division algorithm for dividing polynomials are: 1) Divide the leading term of the dividend by the leading term of the divisor to obtain the first term of the quotient. 2) Multiply the divisor by the first term of the quotient and subtract the result from the dividend. 3) Bring down the next term of the dividend and repeat the process, dividing the leading term of the new dividend by the leading term of the divisor. 4) Continue this process until the degree of the remainder is less than the degree of the divisor, at which point the division is complete.
• Analyze how the degree of the polynomials involved affects the long division process and the final result.
  • The degree of the polynomials involved in long division is crucial to the process and the final result. The degree of the dividend must be greater than or equal to the degree of the divisor for long division to be possible. Additionally, the degree of the remainder must be less than the degree of the divisor for the division process to be complete. The degree of the quotient will be the difference between the degree of the dividend and the degree of the divisor. Understanding the relationship between the degrees of the polynomials is key to successfully performing and interpreting the results of long division.

Related terms

Polynomial Division: The process of dividing one polynomial by another to find the quotient and remainder.

Synthetic Division:

A shortcut method for dividing a polynomial by a linear expression, where only the coefficients are used in the division process.

Degree of a Polynomial: The highest exponent of the variable in a polynomial.