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Chapter 9: Q83. (page 535)

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

x2+25

Short Answer

Expert verified

x2+25is aprime.

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.

x2+25cannot be written in the form of a2鈭�b2.

03

Step 3. Write the conclusion.

As x2+25 cannot be written in the form of a2鈭�b2, it cannot be factored and therefore, the given polynomial is prime.

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