Introductory Algebra for College Students (7th Edition)

Published by Pearson

Chapter 5 - Section 5.2 - Multiplying Polynomials - Exercise Set - Page 359: 73

Answer

$x^4+3x^3+5x^2+7x+4$

Work Step by Step

Using the Distributive Property, the given expression, $(x+1)(x^3+2x^2+3x+4) ,$ is equivalent to \begin{array}{l}\require{cancel} x(x^3)+x(2x^2)+x(3x)+x(4)+1(x^3)+1(2x^2)+1(3x)+1(4) \\\\= x^4+2x^3+3x^2+4x+x^3+2x^2+3x+4 \\\\= x^4+(2x^3+x^3)+(3x^2+2x^2)+(4x+3x)+4 \\\\= x^4+3x^3+5x^2+7x+4 .\end{array}

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