Question

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)

Answer 1

b

Explanation:

Answer 2

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)`