Chapter 6: Q 6.61 (page 599)

Factor: $x^{3} + 27$ .

Short Answer

Expert verified

Factors of $x^{3} + 27$ are $(x + 3) (x^{2} - 3 x + 9)$ .

Step by step solution

Step 1. Given information.

Given an expression $x^{3} + 27$ .

Step 2. Check if it is a sum or difference of cubes pattern.

It can be seen that $x^{3} + 27 = x^{3} + 3^{3}$ .

The expression is sum of cubes pattern.

Step 3. Use either the sum or difference of cubes pattern and simplify.

Note that $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ .

The expression is sum of cubes.

$\begin{array}{rcl} x^{3} + 27 & = & x^{3} + 3^{3} \\ = & (x + 3) (x^{2} - 3 x + 9) \end{array}$

So, $x^{3} + 27 = (x + 3) (x^{2} - 3 x + 9)$ .

Step 4. Check by multiplying the factors.

Verify as follows. $\begin{array}{rcl} (x + 3) (x^{2} - 3 x + 9) & = & x (x^{2} - 3 x + 9) + 3 (x^{2} - 3 x + 9) \\ = & x^{3} - 3 x^{2} + 9 x + 3 x^{2} - 9 x + 27 \\ = & x^{3} + 27 \end{array}$

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Factor: $x^{3} + 27$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Check if it is a sum or difference of cubes pattern.

Step 3. Use either the sum or difference of cubes pattern and simplify.

Step 4. Check by multiplying the factors.

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Factor:x3+27.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Check if it is a sum or difference of cubes pattern.

Step 3. Use either the sum or difference of cubes pattern and simplify.

Step 4. Check by multiplying the factors.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Applied Mathematics

Calculus

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

Factor: $x^{3} + 27$ .