   Chapter A.4, Problem 10E 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 - 9 x + 14

To determine

To factor:

The trinomial x2-9x+14.

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,

x2-9x+14.

First look for a common factor (GCF) of the terms x2, -9x and 14.

But, the GCF is 1.

Now, let us factorize the given expression x2-9x+14 by the reverse FOIL method.

First factorize the last constant term (+14) of the expression such that the sum of the factors gives the coefficient of the middle term (-9).

Thus, factorize -14 as -7, -2 such that the sum of the factors -7+-2 gives -9.

Now, split the middle term -9x as -7x+-2x

Hence the given expression becomes

x2-9x+14

=x2+-7x+-2x+14

=x·x+-7·x±2·<

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