Chapter 6: Q. 130E (page 590)

In the following exercises, factor using substitution. $x^{2} - 13 x^{2} - 30$

Short Answer

Expert verified

The factors are $(x^{2} + 2) (x^{2} - 15)$

Step by step solution

Step 1. Given Information

The trinomial is $x^{4} - 13 x^{2} - 30$

Find factors using substitution method.

Step 2. Find the term for substitution

Rewrite the trinomial to prepare for the substitution

${(x^{2})}^{2} - 13 x^{2} - 30$

Substitute

$x^{2} = u$

So, trinomial becomes,

$u^{2} - 13 u - 30$

Step 3. Factor the trinomial.

Split the middle term of trinomial to find factors

$u^{2} + 2 u - 15 u - 30$

Factor it

$u (u + 2) - 15 (u + 2) (u + 2) (u - 15)$

Step 4. Substitute back u

Substitute back $u = x^{2}$

$(x^{2} + 2) (x^{2} - 15)$

Step 5. Check

Multiply all factors

$(x^{2} + 2) (x^{2} - 15) x^{4} + 2 x^{2} - 15 x^{2} - 15 x^{4} - 13 x^{2} - 15$

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In the following exercises, factor using substitution. $x^{2} - 13 x^{2} - 30$

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 substitution.x2−13x2-30

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

Statistics

Pure Maths

Geometry

Discrete Mathematics

Logic and Functions

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, factor using substitution. $x^{2} - 13 x^{2} - 30$