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Ch. 3 - Polynomial and Rational Functions
Blitzer - College Algebra 8th Edition
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Tutti i libri di testoBlitzer 8th EditionCh. 3 - Polynomial and Rational FunctionsProblema 53
Capitolo 4, Problema 53

Write a polynomial that represents the length of each rectangle. Transcription: The area of the rectangle is 0.5x3 - 0.3x2 + 0.22x + 0.06 square units and its width is x + 0.2 units
Rectangle with width x + 0.2 units and area 0.5x^3 - 0.3x^2 + 0.22x + 0.06 square units.

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1
Recall the formula for the area of a rectangle: \(\text{Area} = \text{Length} \times \text{Width}\).
Given the area as \(0.5x^{3} - 0.3x^{2} + 0.22x + 0.06\) and the width as \(x + 0.2\), set up the equation: \(0.5x^{3} - 0.3x^{2} + 0.22x + 0.06 = \text{Length} \times (x + 0.2)\).
To find the length, divide the area polynomial by the width polynomial: \(\text{Length} = \frac{0.5x^{3} - 0.3x^{2} + 0.22x + 0.06}{x + 0.2}\).
Perform polynomial division (either long division or synthetic division) to divide \(0.5x^{3} - 0.3x^{2} + 0.22x + 0.06\) by \(x + 0.2\).
The quotient from this division will be the polynomial expression representing the length of the rectangle.

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Polynomial Expressions

A polynomial is an algebraic expression consisting of terms with variables raised to non-negative integer powers and coefficients. Understanding how to manipulate polynomials, including addition, subtraction, multiplication, and division, is essential for working with expressions like the given area and width.
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Introduction to Algebraic Expressions

Area of a Rectangle

The area of a rectangle is found by multiplying its length by its width. Given the area and one dimension (width), you can find the other dimension (length) by dividing the area polynomial by the width polynomial.
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Systems of Inequalities

Polynomial Division

Polynomial division is the process of dividing one polynomial by another, similar to numerical long division. It is used here to find the length polynomial by dividing the area polynomial by the width polynomial.
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Introduction to Polynomials
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