Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 3 - Exponents, Polynomials and Functions - 3.5 Special Factoring Techniques - 3.5 Exercises: 38

Answer

$(3k^3+7)(k^3+4)$

Work Step by Step

The trinomial is not a perfect square, so we must use a different method. To factor when the coefficient of the first term is greater than $1$, determine the two numbers that, when multiplied, equal the coefficient of the first term times the third term, and, when added, equal the coefficient of the middle term. Next, group the four terms into two sets of parentheses and pull out the greatest common factors in each. $3k^6+19k^3+28$ $=3k^6+12k^3+7k^3+28$ $=(3k^6+12k^3)+(7k^3+28)$ $=3k^3(k^3+4)+7(k^3+4)$ $=(3k^3+7)(k^3+4)$
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