Domanda del libro di testo
In Exercises 1–6, find all numbers that must be excluded from the domain of each rational expression. (x+5)/(x2−25)
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Ch. P - Fundamental Concepts of Algebra
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 1, Problema 3
Is the algebraic expression a polynomial? If it is, write the polynomial in standard form. (2x+3)/x
Guida verificata passo dopo passo1
Identify the given expression: \(\frac{2x + 3}{x}\).
Recall that a polynomial is an expression consisting of variables raised to non-negative integer powers, combined using addition, subtraction, and multiplication only. Division by a variable (like \(x\)) is not allowed in polynomials.
Rewrite the expression by dividing each term in the numerator by \(x\): \(\frac{2x}{x} + \frac{3}{x}\).
Simplify the terms: \(\frac{2x}{x} = 2\) and \(\frac{3}{x} = 3x^{-1}\).
Since \(3x^{-1}\) has a negative exponent, the expression is not a polynomial. Therefore, it cannot be written in standard polynomial form.
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Definition of a Polynomial
A polynomial is an algebraic expression consisting of variables and coefficients, involving only non-negative integer exponents of variables combined using addition, subtraction, and multiplication. Expressions with variables in denominators or with negative or fractional exponents are not polynomials.
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Introduction to Polynomials
Standard Form of a Polynomial
The standard form of a polynomial arranges terms in descending order of their exponents, starting with the highest degree term. This format helps in easily identifying the degree and leading coefficient of the polynomial.
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05:16Standard Form of Polynomials
Simplifying Rational Expressions
A rational expression is a ratio of two polynomials. To determine if it is a polynomial, simplify the expression by performing division or factoring. If the variable remains in the denominator after simplification, the expression is not a polynomial.
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05:07Simplifying Algebraic Expressions
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