EXAMPLE 3Multiplying PolynomialsFind the product: (2x + 3)(x² - 5x + 4)

Answered: EXAMPLE 3 Multiplying Polynomials Find…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

ChapterP: Prerequisites

SectionP.5: Algebraic Expressions

Problem 26E

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Building Envelope The building code in a certain town requires that a house be at least 10 ft from the boundaries of the lot. The buildable area or building envelope for the rectangular lot shown in the following figure is given by A=(x20)(y20) a Explain how the expression for A is obtained. b Expand to express A as a polynomial in x and y. c A contractor has a choice of purchasing one of two rectangular lots, each having the same area. One lot measures 100 ft by 400 ft; the other measures 200 ft by 200 ft. Which lot has the larger building envelope?
Polynomials Complete the following table by stating whether the polynomial is a monomial, binomial, or trinomial; then list it terms and state its degree.
In Exercises 2-6, fill in the blanks. A shortcut for long division of polynomials is ,in which the divisor must be of the form xk.
DISCUSS: Degrees of Sums and Products of Polynomials Make up several pairs of polynomials, then calculate the sum and product of each pair. On the basis of your experiments and observations, answer the following questions. (a) How is the degree of the product related to the degrees of the original polynomials? (b)How is the degree of the sum related to the degrees of the original polynomials? (c) Test your conclusions by finding the sum and product of the following polynomials: 2x3+x3 and 2x3x+7
CONCEPTS To subtract polynomials, we subtract terms. So (2x3+9x2+x+10)(x3+x2+6x+8)=.

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EXAMPLE 3 Multiplying Polynomials Find the product: (2x + 3)(x² - 5x + 4)