Chapter A.4, Problem 22E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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 6a2c211a2bc2âˆ’10b2c2 2â‹…3â‹…aâ‹…aâ‹…câ‹…câ€‰â€‰â€‰â€‰â€‰11â‹…aâ‹…bâ‹…câ‹…c2â‹…â€‰â€‰â€‰5â‹…bâ‹…bâ‹…câ‹…câ‹…(âˆ’1)

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

The given expression can be expressed as

6a2c2+11abc2-10b2c2

=c2Â·6a2+c2Â·11ab-c2Â·10b2.

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

By the reverse of the distributive property of multiplication,

=c2Â·(6a2+11ab-10b2)

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

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