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Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=2x2−8x+3
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Ch. 3 - Polynomial and Rational Functions
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
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)
Guida verificata passo dopo passo1
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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05:13
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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05:16Standard 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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05:13Introduction to Polynomials
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