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: 59

Answer

prime

Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the given expression, $ 4t^2-3t+15 ,$ find two numbers whose product is $ac$ and whose sum is $b$ in the quadratic expression $ax^2+bx+c.$ Use these $2$ numbers to decompose the middle term of the given quadratic expression and then use factoring by grouping. $\bf{\text{Solution Details:}}$ Using factoring of trinomials, the value of $ac$ in the trinomial expression above is $ 4(15)=60 $ and the value of $b$ is $ -3 .$ There are no $2$ numbers that have a product of $ac$ and a sum of $b.$ Hence the given trinomial is not factorable or it is $\text{ prime .}$
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