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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Chapter
Section
BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 9 to 16, factor each trinomial product.

y 2 - 4 y - 96

To determine

To factor:

The trinomial y2-4y-96.

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,

y2-4y-96

First look for a common factor (GCF) of the terms y2, -4y and -96.

But, the GCF is 1.

Now, let us factorize the given expression y2-4y-96 by the reverse FOIL method.

First factorize the last constant (-96) of the expression such that the sum of the factors gives the coefficient of the middle term (-4).

Thus, factorize -96 as -12·8 such that the sum of the factors (-12+8) gives -4.

Now, split the middle term -4y as -12y+8y

Hence the given expression becomes

=y2-4y-96

=y2-12y+8y-96

=y·y+

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