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Chapter A.4, Problem 21E
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### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

#### Solutions

Chapter
Section
BuyFindarrow_forward

### Elementary Geometry For College St...

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

# In Exercises 17 to 22, factor completely.  2 a x 2 + 3 a x - 35 a

To determine

To factor completely:

2ax2+3ax-35a.

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,

2ax2+3ax-35a.

First look for a common factor (GCF) of the terms 2ax2, 3ax and -35a.

 Terms Prime factors 2ax23axâˆ’35a â€‰2â‹…aâ‹…xâ‹…xâ€‰â€‰â€‰â€‰â€‰3â‹…aâ‹…x7â‹…â€‰5â‹…aâ‹…(âˆ’1)

Thus, the GCF of the terms 2ax2, 3ax and -35a is â€˜aâ€™.

The given expression can be expressed as

2ax2+3ax-35a.

=aÂ·2x2+aÂ·3x+aÂ·(-35)

Here, â€˜aâ€™ is distributed over the expression 2x2+3x-35.

By the reverse of distributive property of multiplication,

=aÂ·2x2+3x-35

Now, factor the expression 2x2+3x-35 by the reverse FOIL method

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