   Chapter A.4, Problem 19E 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 17 to 22, factor completely. 3 y 2 + 24 y + 45

To determine

To factor completely:

3y2+24y+45

Explanation

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,

3y2+24y+45

First look for a common factor GCF of the terms 3y2, 24y and 45.

 Terms Prime factors 3y224y45 3⋅y⋅y3⋅2⋅2⋅2⋅y3⋅3⋅5

Thus, the GCF of the terms 3y2, 24y and 45 is 3.

The given expression can be expressed as

3y2+24y+45

=3·y2+3·8y+3·15

Here, 3 is distributed over the expression y2+8y+15. By the reverse of distributive property of multiplication,

=3·y2+8y+15

Now, factor the expression y2+8y+15 by the reverse FOIL method

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