   Chapter A.4, Problem 9E 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 9 to 16, factor each trinomial product. x 2 + 7 x + 12

To determine

To factor:

The trinomial x2+7x+12

Explanation

Approach:

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,

x2+7x+12

First look for a common factor GCF of the terms x2, 7x and 12.

But, the GCF is 1.

Now, let us factorize the given expression x2+7x+12 by trial and error method.

The factored from of

x2+7x+12 is x+?x+?.

Now, find the test combinations that lead to the last term 12.

12=1·12

12=2·6

12=3·4

Of the above three group of test combinations let us try with the factors 1 and 12.

Thus, we have

=x+1x+12

Multiply; each term of the first factor with each term of the second factor.

=x·x+x·12+1·x+1·12

=x2+12x+x+12

Combine; the like terms together.

=x2+12x+x+12

=x2+13x+12, which is false

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