Chapter 9: Q83. (page 535)

Factor each polynomial if possible. If the polynomial cannot be factored, write prime.
$x^{2} + 25$

Short Answer

Expert verified

$x^{2} + 25$ is aprime.

Step by step solution

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

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

$(a + b) (a - b) = a^{2} - b^{2}$

Step 2. Write in terms of a2−b2.

Write the given polynomial in terms of $a^{2} - b^{2}$ .

$x^{2} + 25$ cannot be written in the form of $a^{2} - b^{2}$ .

Step 3. Write the conclusion.

As $x^{2} + 25$ cannot be written in the form of $a^{2} - b^{2}$ , it cannot be factored and therefore, the given polynomial is prime.

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Factor each polynomial if possible. If the polynomial cannot be factored, write prime.
$x^{2} + 25$

Short Answer

Step by step solution

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

Step 2. Write in terms of a2−b2.

Step 3. Write the conclusion.

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Factor each polynomial if possible. If the polynomial cannot be factored, write prime.x2+25

Short Answer

Step by step solution

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

Step 2. Write in terms of a2−b2.

Step 3. Write the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Theoretical and Mathematical Physics

Statistics

Mechanics Maths

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Factor each polynomial if possible. If the polynomial cannot be factored, write prime.
$x^{2} + 25$