Chapter 6: Q. 457 (page 638)

In the following exercises, factor completely.
$6 x^{4} - 19 x^{2} + 15$

Short Answer

Expert verified

On factoring, we get $(3 x^{2} - 5) (2 x^{2} - 3)$ .

Step by step solution

Step 1. Given information.

Consider the given question,

$6 x^{4} - 19 x^{2} + 15$

Rewrite the trinomial to prepare for the substitution,

$= 6 {(x^{2})}^{2} - 19 x^{2} + 15 . . . . . . (i)$

Assume $u = x^{2}$ and substitute in equation (i),

$= 6 u^{2} - 19 u + 15$

Factor out the trinomial,

role="math" localid="1644848571301" $= 6 u^{2} - 9 u - 10 u + 15 = 3 u (2 u - 3) - 5 (2 u - 3) = (3 u - 5) (2 u - 3) . . . . . . (i i)$

Substitute $u = x^{2}$ in equation (ii),

$= (3 x^{2} - 5) (2 x^{2} - 3)$

Step 2. Check the answers.

Check by multiplying,

= (3 x^{2} - 5) (2 x^{2} - 3) = 6 x^{4} - 9 x^{2} - 10 x^{2} + 15 = 6 x^{4} - 19 x^{2} + 15

This is true.

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In the following exercises, factor completely.
$6 x^{4} - 19 x^{2} + 15$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Check the answers.

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In the following exercises, factor completely.6x4-19x2+15

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Check the answers.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Discrete Mathematics

Calculus

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, factor completely.
$6 x^{4} - 19 x^{2} + 15$