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Chapter 6: Q. 152E (page 590)

In the following exercises, factor each expression using any methodx4-7x2鈭�8

Short Answer

Expert verified

The factors arex2+1x2-8

Step by step solution

01

Step 1. Given Information

The trinomial isx4-7x2鈭�8

Find factors using substitution method.

02

Step 2. Find the term for substitution

Rewrite the trinomial to prepare for the substitution

x22-7x2鈭�8

Substitutex2=u

So, trinomial becomesu2-7u-8

03

Step 3. Factor the trinomial

Split the middle term of trinomial to find factors

u2+u-8u-8

Factor it

uu+1-8u+1u+1u-8

04

Step 4. Substitute back u

Substitute back u=x2

role="math" localid="1644897103752" x2+1x2-8

05

Step 5. Check

Multiply all factors x2+1x2-8

x4+x2-8x2-8x4-7x2-8

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