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Chapter 9: Q82. (page 535)

Factor each polynomial if possible. If the polynomial cannot be factored, write prime.

n2鈭�16

Short Answer

Expert verified

The factors n2鈭�16 are n+4n鈭�4.

Step by step solution

01

Step 1. Write the property of the product of sum and difference.

The product of a+band a-b is the square of a the minus square of b, that is,

a+ba鈭�b=a2鈭�b2

02

Step 2. Write in terms of a2−b2.

Write the given polynomial in terms of a2鈭�b2.

n2鈭�42

03

Step 3. Factor the difference of squares.

Factors the difference of squares, that is, n2鈭�42.

n+4n鈭�4.

Therefore, the factors of n2鈭�16are n+4n鈭�4.

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