Chapter 9: Q82. (page 535)

Factor each polynomial if possible. If the polynomial cannot be factored, write prime.
$n^{2} - 16$

Short Answer

Expert verified

The factors $n^{2} - 16$ are $(n + 4) (n - 4)$ .

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 $a^{2} - b^{2}$ .

$n^{2} - 4^{2}$

Step 3. Factor the difference of squares.

Factors the difference of squares, that is, $n^{2} - 4^{2}$ .

$(n + 4) (n - 4)$ .

Therefore, the factors of $n^{2} - 16$ are $(n + 4) (n - 4)$ .

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Factor each polynomial if possible. If the polynomial cannot be factored, write prime.
$n^{2} - 16$

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. Factor the difference of squares.

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Factor each polynomial if possible. If the polynomial cannot be factored, write prime.n2−16

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. Factor the difference of squares.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Statistics

Pure Maths

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Factor each polynomial if possible. If the polynomial cannot be factored, write prime.
$n^{2} - 16$