   Chapter A.4, Problem 21E 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.  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 2ax23ax−35a 2⋅a⋅x⋅x     3⋅a⋅x7⋅ 5⋅a⋅(−1)

Thus, the GCF of the terms 2ax2, 3ax and -35a is ‘a’.

The given expression can be expressed as

2ax2+3ax-35a.

=a·2x2+a·3x+a·(-35)

Here, ‘a’ is distributed over the expression 2x2+3x-35.

By the reverse of distributive property of multiplication,

=a·2x2+3x-35

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

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