Question

Divide using synthetic division. $$ \left(x^{4}-2 x^{3}+x^{2}+x-1\right) \div(x-1) $$

   Divide using synthetic division.
$$
\left(x^{4}-2 x^{3}+x^{2}+x-1\right) \div(x-1)
$$

Algebra 2

Prentice Hall, Basia… 1st Edition

Chapter 6, Problem 52

Instant Answer

Solved by Expert K B

08/26/2019

Step 1

We also write down the root of the divisor, which is 1 (since x - 1 = 0 when x = 1). Show more…

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Divide using synthetic division. $$ \left(x^{4}-2 x^{3}+x^{2}+x-1\right) \div(x-1) $$

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Key Concepts

Polynomial Division

Polynomial division is the process of dividing a polynomial by another polynomial to obtain a quotient and possibly a remainder. It is analogous to integer division and can be performed using methods such as long division or synthetic division. Understanding polynomial division is essential for factorization, solving polynomial equations, and studying the behavior of functions.

Remainder Theorem

The Remainder Theorem states that when a polynomial f(x) is divided by a binomial of the form (x - c), the remainder is equal to f(c). This theorem not only provides a quick way to determine the remainder without performing full division but also plays an important role in polynomial factorization and root finding.

Synthetic Division

Synthetic division is a simplified method of dividing a polynomial by a binomial of the form (x - c). This method involves using only the coefficients of the polynomial, streamlining calculations compared to the long division approach, and is particularly useful for finding a quotient and remainder quickly when dividing by a linear divisor.

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