Q. 128E In the following exercises, fact... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 6: Q. 128E (page 590)

In the following exercises, factor using substitution.
$x^{4} + 2 x^{2} 鈭� 8$

Short Answer

Expert verified

The factors are $(x^{2} + 4) (x^{2} - 2)$

Step by step solution

Step 1. Given Information

The trinomial is $x^{4} + 2 x^{2} 鈭� 8$ .

Find factors using substitution method.

Step 2. Find the term for substitution

Rewrite the trinomial to prepare for the substitution ${(x^{2})}^{2} + 2 x^{2} - 8$

Substitute $x^{2} = u$

So, trinomial becomes $u^{2} + 2 u - 8$

Step 3. Factor the trinomial

Split the middle term of trinomial to find factors

$u^{2} - 2 u + 4 u - 8$

Factor it

$u (u - 2) + 4 (u - 2)$

$(u - 2) (u + 4)$

Step 4. Substitute back u

Substitute back $u = x^{2}$

$(x^{2} + 4) (x^{2} - 2)$

Step 5. Check

Multiply all factors

$(x^{2} + 4) (x^{2} - 2)$

$x^{4} + 4 x^{2} - 2 x^{2} - 8 x^{4} + 2 x^{2} - 8$

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91影视

In the following exercises, factor using substitution.
$x^{4} + 2 x^{2} 鈭� 8$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find the term for substitution

Step 3. Factor the trinomial

Step 4. Substitute back u

Step 5. Check

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91影视

In the following exercises, factor using substitution.x4+2x2鈭�8

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find the term for substitution

Step 3. Factor the trinomial

Step 4. Substitute back u

Step 5. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Discrete Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, factor using substitution.
$x^{4} + 2 x^{2} 鈭� 8$