Chapter 6: Q. 129E (page 590)

In the following exercises, factor using substitution $x^{4} - 3 x^{2} - 2$

Short Answer

Expert verified

The factors are $(x^{2} - 7) (x^{2} + 4)$

Step by step solution

Step 1. Given Information

The trinomial is $x^{4} - 3 x^{2} - 2$

Find factors using substitution method.

Step 2. Find the term for substitution

Rewrite the trinomial to prepare for the substitution

${(x^{2})}^{2} - 3 x^{2} - 28$

Substitute $x^{2} = u$

So, trinomial becomes $u^{2} - 3 u - 28$

Step 3. Factor the trinomial

Split the middle term of trinomial to find factors

$u^{2} - 7 u + 4 u - 28$

Factor it

$u (u - 7) + 4 (u - 7) (u - 7) (u + 4)$

Step 4. Substitute back u

Substitute back $u = x^{2}$

$(x^{2} - 7) (x^{2} + 4)$

Step 5. Check

Multiply all factors

$(x^{2} - 7) (x^{2} + 4) x^{4} - 7 x^{2} + 4 x^{2} - 28 x^{4} - 3 x^{2} - 28$

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In the following exercises, factor using substitution $x^{4} - 3 x^{2} - 2$

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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In the following exercises, factor using substitutionx4−3x2-2

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

Applied Mathematics

Calculus

Statistics

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

In the following exercises, factor using substitution $x^{4} - 3 x^{2} - 2$