Domanda del libro di testo
Use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=2x3−11x2+7x−5;f(4)
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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 32
Given f(x) = 2x^3 - 7x^2 + 9x - 3, use the Remainder Theorem to find f(- 13).
Guida verificata passo dopo passo1
Identify the polynomial function given: \( f(x) = 2x^3 - 7x^2 + 9x - 3 \).
According to the Remainder Theorem, the remainder of the division of \( f(x) \) by \( x - c \) is \( f(c) \).
In this problem, we need to find \( f(-13) \), so \( c = -13 \).
Substitute \( x = -13 \) into the polynomial: \( f(-13) = 2(-13)^3 - 7(-13)^2 + 9(-13) - 3 \).
Calculate each term separately and then sum them to find the remainder, which is \( f(-13) \).
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Remainder Theorem
The Remainder Theorem states that for a polynomial function f(x), the remainder of the division of f(x) by (x - c) is equal to f(c). This theorem allows us to evaluate the polynomial at a specific point without performing long division, simplifying the process of finding function values.
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05:10
Higher Powers of i
Polynomial Functions
A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. In this case, f(x) = 2x^3 - 7x^2 + 9x - 3 is a cubic polynomial, which means it has a degree of 3 and can have up to three real roots. Understanding the structure of polynomial functions is essential for applying the Remainder Theorem.
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06:04Introduction to Polynomial Functions
Function Evaluation
Function evaluation involves substituting a specific value into a function to determine its output. In this context, evaluating f(-13) means replacing x in the polynomial with -13 and calculating the resulting value. This process is fundamental in applying the Remainder Theorem to find the remainder when the polynomial is evaluated at a given point.
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4:26Evaluating Composed Functions
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