Chapter 7: Q. 310 (page 878)

In the following exercises, factor completely.
$3 v^{4} - 768$

Short Answer

Expert verified

The factored form of the polynomial is $3 (v - 4) (v + 4) (v^{2} + 16) .$

Step by step solution

Step 1. Given Information.

The given polynomial is $3 v^{4} - 768 .$

Step 2. Factoring

Let's find the GCF and factor out the GCF,

$3 (v^{4} - 256)$

In the parentheses, the polynomial is a binomial and it is the type of the difference of squares.

To factor, the given polynomial completely writes it as a product of conjugates.

So,

$3 (v^{4} - 256) = 3 \{{(v^{2})}^{2} - {(16)}^{2}\} = 3 \{(v^{2} - 16) (v^{2} + 16)\} = 3 \{{(v)}^{2} - {(4)}^{2}\} (v^{2} + 16) = 3 (v - 4) (v + 4) (v^{2} + 16)$

The polynomial is factored completely.

Thus, the factored form is $3 (v - 4) (v + 4) (v^{2} + 16) .$

Step 3. Check the answer

To check the answer, expand the factored form we get,

$3 v^{4} - 768 = 3 (v - 4) (v + 4) (v^{2} + 16) 3 v^{4} - 768 = (3 v - 12) (v + 4) (v^{2} + 16) 3 v^{4} - 768 = (3 v^{2} + 12 v - 12 v - 48) (v^{2} + 16) 3 v^{4} - 768 = 3 v^{4} + 48 v^{2} + 12 v^{3} + 192 v - 12 v^{3} - 192 v - 48 v^{2} - 768 3 v^{4} - 768 = 3 v^{4} - 768$

L.H.S = R.H.S

Thus, the answer is right.

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In the following exercises, factor completely.
$3 v^{4} - 768$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Factoring

Step 3. Check the answer

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In the following exercises, factor completely.3v4−768

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Factoring

Step 3. Check the answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Theoretical and Mathematical Physics

Decision Maths

Discrete Mathematics

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, factor completely.
$3 v^{4} - 768$