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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 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 3yy3222y335

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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