Chapter A.4, Problem 14E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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. 12 a 2 + 31 a + 20

To determine

To factor:

The trinomial 12a2+31a+20

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,

12a2+31a+20

First look for a common factor (GCF) of the terms 12a2, 31a and 20.

But, the GCF is 1.

Now, let us factorize the given expression 12a2+31a+20 by the reverse FOIL method.

First factorize the product of the coefficient of the first term and the constant, such that the sum term of the factors gives the coefficient of the middle term.

Thus, factorize 240 as 16Â·15, such that the sum of the factors (16+15) gives 31.

Now, split the middle term 31a as 16a+15a

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