   Chapter A.4, Problem 23E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 23 to 24, find the three factors for the cubic trinomials.  x 3 + 5 x 2 + 4 x

To determine

The three factors of the cubic trinomials

x3+5x2+4x.

Explanation

Factorizing a polynomial is to express the polynomial as a product of simpler expressions such that each of the simpler expressions divides the polynomial completely and also the product of all the simpler expressions gives the polynomial.

Calculation:

Given,

x3+5x2+4x

First look for the common factor (GCF) of the terms x3, 5x2 and 4x.

 Terms Prime factors x35x24x x⋅x⋅x5⋅x⋅x4⋅ x

Thus, the GCF of the terms x3, 5x2 and 4x is x.

The given expression can be expressed as

x3+5x2+4x

=x·x2+x·5x+x·4

Here, x is distributed over the expression x2+5x+4. By the reverse of the distributive property of multiplication,

x·(x2+5x+4)

Now, factor the expression x2+5x+4 by the reverse FOIL method

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