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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Section
BuyFindarrow_forward

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 xxx5xx4x

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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