## Elementary Algebra

Published by Cengage Learning

# Chapter 5 - Exponents and Polynomials - 5.3 - Multiplying Polynomials - Problem Set 5.3 - Page 207: 33

#### Answer

$x^{4}$ + 7$x^{3}$ + 17$x^{2}$ + 23x + 12

#### Work Step by Step

($x^{2}$ + 2x + 3)($x^{2}$ + 5x + 4) = Use the distributive property. $x^{2}$($x^{2}$) +$x^{2}$(5x) +$x^{2}$(4) +2x($x^{2}$) +2x(5x) +2x(4) +3($x^{2}$) +3(5x) +3(4) = $x^{4}$ + 5$x^{3}$ + 4$x^{2}$ + 2$x^{3}$ + 10$x^{2}$ + 8x + 3$x^{2}$ + 15x + 12 = Simplify. $x^{4}$ + 7$x^{3}$ + 17$x^{2}$ + 23x + 12

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