   Chapter A.4, Problem 22E 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 17 to 22, factor completely. 6 a 2 c 2 + 11 a b c 2 - 10 b 2 c 2

To determine

To factor completely:

6a2c2+11abc2-10b2c2.

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,

6a2c2+11abc2-10b2c2

First look for the common factor (GCF) of the terms 6a2c2, 11abc2 and -10b2c2.

 Terms Prime factors 6a2c211a2bc2−10b2c2 2⋅3⋅a⋅a⋅c⋅c     11⋅a⋅b⋅c⋅c2⋅   5⋅b⋅b⋅c⋅c⋅(−1)

Thus, the GCF of the terms 6a2c2, 11abc2 and -10b2c2 is c·c=c2

The given expression can be expressed as

6a2c2+11abc2-10b2c2

=c2·6a2+c2·11ab-c2·10b2.

Here, c2 is distributed over the expression 6a2+11ab-10b2.

By the reverse of the distributive property of multiplication,

=c2·(6a2+11ab-10b2)

Now, factor the expression 6a2+11ab-10b2 by the reverse FOIL method

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