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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. 127E (page 590)

In the following exercises, factor using substitution. $x^{4} 鈭� x^{2} - 12$

Short Answer

Expert verified

The factors are $(x^{2} + 3) (x - 2) (x + 2)$

Step by step solution

01

Step 1. Given information

The trinomial to factor is $x^{4} 鈭� x^{2} - 12$ .

Use substitution method.

02

Step 2. Find term for substitution

Rewrite the trinomial to prepare for the substitution

${(x^{2})}^{2} - x^{2} - 12$

Substitute $x^{2} = u$ and rewrite the trinomial

$u^{2} - u - 12$

03

Step 3. Factor the trinomial

Split the middle term of trinomial to find factors

$u^{2} + 3 x - 4 x - 12$

$u (u + 3) - 4 (u + 3) (u + 3) (u - 4)$

04

Step 4. Substitute back u

Substitute back $u = x^{2}$

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

$x^{2} - 4$ further factor as $(x + 2) (x - 2)$

So factors are $(x^{2} + 3) (x - 2) (x + 2)$

05

Step 5. Check

Multiply all the factors $(x^{2} + 3) (x - 2) (x + 2)$

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

again multiply

role="math" localid="1644591950467" $x^{4} + 3 x^{2} - 4 x^{2} - 12 x^{4} - x^{2} - 12$

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Most popular questions from this chapter

Factor by Grouping
In the following exercises, factor by grouping.

$m n 鈭� 6 m 鈭� 4 n + 24$ .

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