Chapter 7: Q. 298 (page 878)

In the following exercises, factor completely.
$5 t^{3} - 40$

Short Answer

Expert verified

The factored form of the polynomial is $5 t^{3} - 40 = 5 (t - 2) (t^{2} + 2 t + 4) .$

Step by step solution

Step 1. Given Information.

The given Polynomial is $5 t^{3} - 40 .$

Step 2. Factoring by the formula for the difference of cubes.

Terms of a polynomial have a common factor $5 .$

$5 t^{3} - 40 = 5 (t^{3} - 8)$

In the parentheses, it is a binomial of the difference of cubes.

Factorize it by using the formula for the difference of cubes.

$5 t^{3} - 40 = 5 (t^{3} - 8) 5 t^{3} - 40 = 5 (t^{3} - 2^{3}) 5 t^{3} - 40 = 5 (t - 2) (t^{2} + 2 t + 2^{2}) 5 t^{3} - 40 = 5 (t - 2) (t^{2} + 2 t + 4)$

Polynomial cannot be factored further.

So factored form islocalid="1647946607143" role="math" $5 t^{3} - 40 = 5 (t - 2) (t^{2} + 2 t + 4) .$

Step 3. Verification.

Check whether the expanded form of the factored polynomial is equal to the original polynomial or not.

$5 t^{3} - 40 = 5 (t - 2) (t^{2} + 2 t + 4) 5 t^{3} - 40 = 5 [t (t^{2} + 2 t + 4) - 2 (t^{2} + 2 t + 4)] 5 t^{3} - 40 = 5 [t^{3} + 2 t^{2} + 4 t - 2 t^{2} - 4 t - 8] 5 t^{3} - 40 = 5 (t^{3} - 8) 5 t^{3} - 40 = 5 t^{3} - 40$

The left-hand side is equal to the right-hand side so factored form is correct.

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In the following exercises, factor completely.
$5 t^{3} - 40$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Factoring by the formula for the difference of cubes.

Step 3. Verification.

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In the following exercises, factor completely.5t3-40

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Factoring by the formula for the difference of cubes.

Step 3. Verification.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Geometry

Statistics

Applied Mathematics

Discrete Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, factor completely.
$5 t^{3} - 40$