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Chapter 6: Q. 457 (page 638)

In the following exercises, factor completely.

6x4-19x2+15

Short Answer

Expert verified

On factoring, we get 3x2-52x2-3.

Step by step solution

01

Step 1. Given information.

Consider the given question,

6x4-19x2+15

Rewrite the trinomial to prepare for the substitution,

=6x22-19x2+15......(i)

Assume u=x2 and substitute in equation (i),

=6u2-19u+15

Factor out the trinomial,

role="math" localid="1644848571301" =6u2-9u-10u+15=3u2u-3-52u-3=3u-52u-3......(ii)

Substitute u=x2in equation (ii),

=3x2-52x2-3

02

Step 2. Check the answers.

Check by multiplying,

=3x2-52x2-3=6x4-9x2-10x2+15=6x4-19x2+15

This is true.

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