   Chapter A.4, Problem 13E 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. 6 y 2 + 5 y - 6

To determine

To factor:

The trinomial 6y2+5y-6.

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,

6y2+5y-6

First look for a common factor (GCF) of the terms 6y2, 5y and -6.

But, the GCF is 1.

Now, let us factorize the given expression 6y2+5y-6 by the reverse FOIL method.

First factorize the last term constant (-36) of the expression such that the sum of the factors gives the coefficient of the middle term (5).

Thus, factorize -36 as 9·-4, such that the sum of the factors (9+(-4)) gives 5.

Now, split the middle term 5y as 9y+(-4y).

Hence the given expression becomes

=6y2+5y-6

=6y2+9y+-4y-6

Since; addition is associative,

=3y·2y+3·3y

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