Q9. Factor聽2x4鈭�32聽completely.... [FREE SOLUTION]

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 10: Q9. (page 665)

Factor $2 x^{4} 鈭� 32$ completely.

Short Answer

Expert verified

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

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.

$\begin{array}{l} 2 x^{4} 鈭� 32 = 2 (x^{4} 鈭� 16) \\ = 2 (x^{4} 鈭� 2^{4}) 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌� [2^{4} = 16] \\ = 2 (x^{2 脳 2} 鈭� 2^{2 脳 2}) \\ = 2 [{(x^{2})}^{2} 鈭� {(2^{2})}^{2}] 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌� [{鲍蝉颈苍驳鈥夆赌墄}^{m 脳 n} = {(x^{m})}^{n}] \\ = 2 [(x^{2} 鈭� 2^{2}) (x^{2} + 2^{2})] 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌� [鲍蝉颈苍驳鈥夆赌夆赌� a^{2} 鈭� b^{2} = (a 鈭� b) (a + b)] \\ = 2 [(x 鈭� 2) (x + 2) (x^{2} + 2^{2})] 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌� [础驳补颈苍产测鈥夆赌夆赌� a^{2} 鈭� b^{2} = (a 鈭� b) (a + b)] \\ = 2 [(x 鈭� 2) (x + 2) (x^{2} + 4)] \\ = 2 (x 鈭� 2) (x + 2) (x^{2} + 4) \end{array}$

Step 3. State the conclusion.

Notice it is not possible to factorize further.

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

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91影视

Factor $2 x^{4} 鈭� 32$ 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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91影视

Factor2x4鈭�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

Applied Mathematics

Mechanics Maths

Decision Maths

Probability and Statistics

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

Factor $2 x^{4} 鈭� 32$ completely.