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Factor completely: 2x4 − 32.

a 2(x2 − 4)(x2 + 4)
b 2(x − 2)(x + 2)(x2 + 4)
c 2(x − 2)(x + 2)(x + 2)(x + 2)
d 2(x − 2)(x + 2)(x2 − 4)

2 Answers

3 votes

Answer:

b

Explanation:

User Edgerunner
by
7.9k points
3 votes

Answer:

Option b) is correct.

The completed factor of given expression is
2(x-2)(x+2)(x^2+4)

Explanation:

Given expression is
2x^4-32

To find the completed factor for the given expression:


2x^4-32:

Taking the common number "2" outside to the above expression we get


2x^4-32=2(x^4-16)

Now rewritting the above expression as below


=2(x^4-2^4) (since 16 can be written as the number 2 to the power of 4)


=2((x^2)^2-(2^2)^2)

The above expression is of the form
a^2-b^2=(a+b)(a-b)

Here
a=x^2 and
b=2^2

Therefore it becomes


=2(x^2+2^2)(x^2-2^2)


=2(x^2+4)(x^2-2^2)

The above expression is of the form
a^2-b^2=(a+b)(a-b)

Here
a=x and
b=2

Therefore it becomes


=2(x^2+4)(x+2)(x-2)


=2(x+2)(x-2)(x^2+4)

Therefore
=2(x+2)(x-2)(x^2+4)


2x^4-32=2(x-2)(x+2)(x^2+4)

Option b) is correct.

The completed factor of given expression is
2(x-2)(x+2)(x^2+4)

User TjerkW
by
9.0k points

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