Question

Perform each division. If there is a nonzero remainder, write the answer in quotient $+\frac{\text { remainder }}{\text { divisor }}$ form. $$\frac{x^{5}-2 x^{3}-3 x^{2}+9}{x^{3}-3}$$

Name: Problem 118, Chapter 0: College Algebra
Uploaded: 2020-09-25T14:38:26-08:00
Duration: 1 min 36 s
Channel: Zain Haider
Description: Perform each division. If there is a nonzero remainder, write the answer in quotient +( remainder )/( divisor ) form. (x^5-2 x^3-3 x^2+9)/(x^3-3)

   Perform each division. If there is a nonzero remainder, write the answer in quotient $+\frac{\text { remainder }}{\text { divisor }}$ form. $$\frac{x^{5}-2 x^{3}-3 x^{2}+9}{x^{3}-3}$$

College Algebra

R. David Gustafson,… 11th Edition

Chapter 0, Problem 118

Instant Answer

Solved by Expert Zain Haider

09/25/2020

Step 1

The first term of the quotient is obtained by dividing the first term of the numerator by the first term of the divisor, i.e., $\frac{x^{5}}{x^{3}} = x^{2}$. Show more…

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Perform each division. If there is a nonzero remainder, write the answer in quotient $+\frac{\text { remainder }}{\text { divisor }}$ form. $$\frac{x^{5}-2 x^{3}-3 x^{2}+9}{x^{3}-3}$$

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Key Concepts

Long Division of Polynomials

Long division of polynomials is a systematic method used to divide one polynomial by another. It mirrors the long division process for numbers, involving steps of dividing, multiplying, subtracting, and then bringing down the next term, ensuring that the remainder has a degree lower than the divisor.

Polynomial Division

Polynomial division is a process in algebra where one polynomial (the dividend) is divided by another polynomial (the divisor), resulting in a quotient and possibly a remainder. This concept is fundamental for simplifying expressions and solving equations involving polynomials.

Division Algorithm for Polynomials

The division algorithm for polynomials states that any polynomial dividend can be expressed as the product of the divisor and a quotient, plus a remainder whose degree is less than that of the divisor. This principle guarantees the uniqueness of the quotient and remainder for a given division problem.

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