Divide. (17 v^3+33 v-18+9 v^4-56 v^2)/(9 v-1)

Name: Problem 52, Chapter 6: Beginning and Intermediate Algebra
Uploaded: 2021-04-13T12:31:02-08:00
Duration: 2 min 13 s
Channel: Erika Bustos
Description: Divide. (17 v^3+33 v-18+9 v^4-56 v^2)/(9 v-1)

Key Concepts

Remainder Theorem

The Remainder Theorem states that when a polynomial is divided by a linear divisor of the form (x - c), the remainder of the division is equal to the value of the polynomial evaluated at x = c. This theorem not only provides a quick check for the correctness of the division result but also interlinks the concepts of polynomial division and function evaluation.

Polynomial Division

This concept involves dividing one polynomial (the dividend) by another (the divisor) to obtain a quotient and possibly a remainder. It is the foundation for understanding how more complex algebraic expressions can be simplified and analyzed through division, analogous to numerical division.

Ordering Polynomials

Ordering polynomials means rewriting them with terms arranged in descending order of degree. This step is crucial when performing polynomial division as it helps in aligning like terms and ensures that the division process is carried out systematically, from the highest to the lowest degree.

Polynomial Long Division

Polynomial long division is a step-by-step procedure used to divide two polynomials. It mirrors the long division process used with numbers and involves determining how many times the divisor fits into the successive parts of the dividend, subtracting the results and bringing down new terms until the division is complete. This method is especially useful when the divisor is not in a form suitable for synthetic division.

Synthetic Division

Synthetic division is a simplified technique for dividing a polynomial by a binomial of the form (x - c). It streamlines the division process by focusing solely on the coefficients and is particularly efficient when the divisor is linear. Adjustments may be necessary when the divisor is not in the standard form, as in cases where leading coefficients differ from one.

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