   Chapter A.4, Problem 15E 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. 3 x 2 + 11 x y - 4 y 2

To determine

To factor:

The trinomial 3x2+11xy-4y2

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,

3x2+11xy-4y2

First look for a common factor (GCF) of the terms 3x2, 11xy and -4y2.

But, the GCF is 1.

Now, let us factorize the given expression 3x2+11xy-4y2 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.

Thus, factorize -12y2 as 12y·-1y such that the sum of the factors (12y+(-1y) gives 11y.

Now, split the middle term 11y as (12xy+-1xy)

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