Chapter 10: Q9. (page 665)

Factor $2 x^{4} - 32$ completely.

Short Answer

Expert verified

The factored form of $2 x^{4} - 32$ is $2 (x - 2) (x + 2) (x^{2} + 4)$ .

Step by step solution

Step 1. State the concept of ‘factorization of polynomial’.

The process of simplifying the polynomial and breaking it into products of its factors is called as the factorization of polynomials.

Step 2. Factor the polynomial 2x4−32.

Factorizing the given polynomial.

$\begin{array}{l} 2 x^{4} - 32 = 2 (x^{4} - 16) \\ = 2 (x^{4} - 2^{4}) [2^{4} = 16] \\ = 2 (x^{2 \times 2} - 2^{2 \times 2}) \\ = 2 [{(x^{2})}^{2} - {(2^{2})}^{2}] [{Using x}^{m \times n} = {(x^{m})}^{n}] \\ = 2 [(x^{2} - 2^{2}) (x^{2} + 2^{2})] [Using a^{2} - b^{2} = (a - b) (a + b)] \\ = 2 [(x - 2) (x + 2) (x^{2} + 2^{2})] [Againby a^{2} - b^{2} = (a - b) (a + b)] \\ = 2 [(x - 2) (x + 2) (x^{2} + 4)] \\ = 2 (x - 2) (x + 2) (x^{2} + 4) \end{array}$

Step 3. State the conclusion.

Notice it is not possible to factorize further.

Therefore, the factorization of $2 x^{4} - 32$ is $2 (x - 2) (x + 2) (x^{2} + 4)$ .

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Factor $2 x^{4} - 32$ completely.

Short Answer

Step by step solution

Step 1. State the concept of ‘factorization of polynomial’.

Step 2. Factor the polynomial 2x4−32.

Step 3. State the conclusion.

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Factor2x4−32completely.

Short Answer

Step by step solution

Step 1. State the concept of ‘factorization of polynomial’.

Step 2. Factor the polynomial 2x4−32.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Logic and Functions

Statistics

Mechanics Maths

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.

Factor $2 x^{4} - 32$ completely.