Chapter 6: Q 187 (page 603)

In the following exercises, factor completely using the difference of squares pattern, if possible.
$16 z^{4} - 1$

Short Answer

Expert verified

The complete factor of ploynomial is $(z - 1) (z + 1) (z^{2} + 1)$ .

Step by step solution

Step 1. Given information

Consider the given ploynomial

$z^{4} - 1$

Step 2. Formula used

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

Step 3. Write the polynomial as squares.

Write the polynomial as perfect squared form.

$z^{4} - 1 = {(z^{2})}^{2} - {(1)}^{2}$

Write them as product of conjugate.

${(z^{2})}^{2} - 1^{2} = (z^{2} - 1^{2}) (z^{2} + 1) = (z - 1) (z + 1) (z^{2} + 1)$

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In the following exercises, factor completely using the difference of squares pattern, if possible.
$16 z^{4} - 1$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Formula used

Step 3. Write the polynomial as squares.

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In the following exercises, factor completely using the difference of squares pattern, if possible.16z4-1

Short Answer

Step by step solution

Step 1. Given information

Step 2. Formula used

Step 3. Write the polynomial as squares.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Decision Maths

Geometry

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, factor completely using the difference of squares pattern, if possible.
$16 z^{4} - 1$