Domanda del libro di testo
Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. (x−1)(x−2)(x−3)≥0
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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 29
In Exercises 27–29, divide using long division.
Guida verificata passo dopo passo1
Write the division in long division format, placing the dividend \(4x^{4} + 6x^{3} + 3x - 1\) under the division bar and the divisor \(2x^{2} + 1\) outside.
Divide the leading term of the dividend \$4x^{4}$ by the leading term of the divisor \$2x^{2}$ to find the first term of the quotient: \(\frac{4x^{4}}{2x^{2}} = 2x^{2}\).
Multiply the entire divisor \(2x^{2} + 1\) by the term \$2x^{2}$ and subtract the result from the dividend to find the new remainder.
Bring down the next terms from the original dividend as needed, then repeat the division process: divide the leading term of the new remainder by \$2x^{2}$, multiply the divisor by this term, and subtract again.
Continue this process until the degree of the remainder is less than the degree of the divisor \(2x^{2} + 1\), then write the quotient and the remainder.
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Polynomial Long Division
Polynomial long division is a method used to divide a polynomial by another polynomial of lower degree, 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 remainder has a lower degree than the divisor.
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Percorso guidato
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 helps determine when to stop the division process, as the division ends when the remainder's degree is less than the divisor's degree.
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Percorso guidato
05:16Standard Form of Polynomials
Like Terms and Polynomial Subtraction
Combining like terms means adding or subtracting terms with the same variable raised to the same power. During polynomial long division, subtracting the product of the divisor and the current quotient term from the dividend requires careful alignment and combination of like terms to simplify the expression correctly.
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Percorso guidato
03:34Adding and Subtracting Polynomials
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Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. n=4; i and 3i are zeros; f(-1) = 20
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Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. 4x2−4x+1≥0
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Domanda del libro di testo
Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. f(x)=x2+3x−10
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