   Chapter A.4, Problem 20E 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. 30 x 2 - 35 + 10

To determine

To factor completely:

30x2-35x+10.

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,

30x2-35x+10.

First look for a common factor GCF of the terms 3x2, -35x and 10.

 Terms Prime factors 30x2−35x10 2⋅3⋅5⋅x⋅x     7⋅5⋅x⋅(−1)     2⋅5

Thus, the GCF of the terms 30x2, -35x and 10 is 5.

The given expression can be expressed as

30x2-35x+10.

=5·6x2-5·7x+5·2

Here, 5 is distributed over the expression 6x2-7x+2. By the reverse of distributive property of multiplication,

=5·(6x2-7x+2)

Now, factor the expression 6x2-7x+2 by the reverse FOIL method.

First factorize the product of the coefficient of the first tern and the constant, such that the sum of the factors gives the coefficient of the middle term

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