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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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In Exercises 9 to 16, factor each trinomial product.

x 2 + 5 x - 24

To determine

To factor:

The trinomial x2+5x-24.

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+5x-24

First look for a common factor (GCF) of the terms x2, 5x and -24.

But, the GCF is 1.

Now, let us factorize the given expression x2+5x-24 by the reverse FOIL method.

First factorize the last constant term (-24) of the expression such that the sum of the factors gives the coefficient of the middle term (5).

Thus, factorize -24 as -3·8, such that the sum of the factors (-3+8) gives 5.

Now, split the middle term 5x as -3x+8x.

Hence the given expression becomes

x2+5x-24

=x2-3x+8x-24

=x·x+-3

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