Domanda del libro di testo
Write an equation in point-slope form and slope-intercept form of the line passing through (-10,3) and (-2,-5).
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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 107
Exercises 107–109 will help you prepare for the material covered in the next section. Factor: x3+3x2−x−3
Guida verificata passo dopo passo1
First, group the terms in pairs to make factoring easier: \(\left(x^{3} + 3x^{2}\right) + \left(-x - 3\right)\).
Next, factor out the greatest common factor (GCF) from each group: from the first group, factor out \(x^{2}\) to get \(x^{2}(x + 3)\); from the second group, factor out \(-1\) to get \(-1(x + 3)\).
Now, notice that both groups contain the common binomial factor \((x + 3)\), so factor this out: \((x + 3)(x^{2} - 1)\).
Recognize that \(x^{2} - 1\) is a difference of squares, which can be factored further as \((x - 1)(x + 1)\).
Write the fully factored form as \((x + 3)(x - 1)(x + 1)\).
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Polynomial Factoring
Factoring polynomials involves rewriting a polynomial as a product of simpler polynomials. This process helps simplify expressions and solve polynomial equations by breaking them down into factors that are easier to work with.
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Introduction to Factoring Polynomials
Grouping Method
The grouping method is a factoring technique where terms in a polynomial are grouped in pairs or sets to find common factors. This method is especially useful for polynomials with four or more terms, allowing you to factor by extracting common binomial factors.
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04:36Factor by Grouping
Rational Root Theorem
The Rational Root Theorem helps identify possible rational roots of a polynomial by considering factors of the constant term and leading coefficient. Testing these roots can simplify factoring by finding zeros that correspond to linear factors.
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04:06Rational Exponents
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