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Ch. 3 - Polynomial and Rational Functions
Blitzer - College Algebra 8th Edition
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Tutti i libri di testoBlitzer 8th EditionCh. 3 - Polynomial and Rational FunctionsProblema 13
Capitolo 4, Problema 13

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (6x3+13x2−11x−15)/(3x2−x−3)

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Identify the dividend and divisor: The dividend is \(6x^{3} + 13x^{2} - 11x - 15\) and the divisor is \(3x^{2} - x - 3\).
Set up the long division by writing the dividend under the division bar and the divisor outside.
Divide the leading term of the dividend, \$6x^{3}$, by the leading term of the divisor, \$3x^{2}$, to find the first term of the quotient: \(\frac{6x^{3}}{3x^{2}} = 2x\).
Multiply the entire divisor \(3x^{2} - x - 3\) by \$2x$ and subtract the result from the dividend to find the new polynomial to bring down.
Repeat the process: divide the new leading term by \$3x^{2}$, multiply the divisor by this term, subtract, and continue until the degree of the remainder is less than the degree of the divisor.

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Polynomial Long Division

Polynomial long division is a method used to divide one polynomial by another, similar to numerical long division. It involves dividing the leading term of the dividend by the leading term of the divisor, multiplying the divisor by this result, subtracting from the dividend, and repeating until the degree of the remainder is less than the divisor.
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Introduction to Polynomials

Degree of a Polynomial

The degree of a polynomial is the highest power of the variable in the expression. Understanding the degree is essential in polynomial division because the division process continues until the remainder's degree is less than the divisor's degree, indicating the division is complete.
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Standard Form of Polynomials

Quotient and Remainder in Polynomial Division

When dividing polynomials, the result consists of a quotient and a remainder. The quotient is the polynomial obtained from the division process, and the remainder is the leftover polynomial with a degree less than the divisor. Expressing the division as dividend = divisor × quotient + remainder is fundamental.
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Introduction to Polynomials
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