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Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728

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BuyFindarrow_forward

Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728
Textbook Problem

For Problems 27 50 , factor each of the following polynomials completely. Indicate any that are not factorable using integers. Don’t forget to look first for a common monomial factor. (Objective 1)

16 x 2 + 25 .

To determine

To factor:

The given polynomials completely and look first for a common monomial factor also indicate any that are not factorable using integers.

Explanation

Approach:

i) Polynomial in the form of The Sum of Two Squares pattern like a2+b2 is not factorable using integers.

ii) The Difference of Two Squares pattern states that a2b2=(a+b)(ab).

The following steps have been followed to find out the complete factors:

Step-1: Find out the common monomial factor in the given polynomial and take out.

Step-2: Find out the given polynomial represents the difference of two squares pattern or the sum of two squares pattern.

Step-3: If it is in the form of the sum of two squares pattern, then it’s not factorable using integers.

Calculation:

1) The given polynomial is 16x2+25.

There is no common monomial factor available in the above polynomial. So, keep the polynomial as it is.

2) The above polynomial can be written as,

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