Question

Factor completely: 2x4 − 32.

Answer 1

Answer:

b

Step-by-step explanation:

Answer 2

Answer:

Option b) is correct.

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

Step-by-step 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  $2(x-2)(x+2)(x^2+4)$