Factors

Aman verma wrote:Q:What are the factors of (x^4+16) ?

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

(B) (x^2+4)(x^2+4)

(C) x(x^2+2)(x^4+4)

(D) (x^2-2)(x^2+2)

(E) Do not exist

This question is poorly worded.

If we're talking about factors (vs. factoring), then the factors should be separated by commas. For example, the factors of 6 are 1, 2, 3 and 6.

EDIT: Removed incorrect info

What's the source of this question?

Cheers,
Brent

Aman verma wrote:

Brent@GMATPrepNow wrote:
This question is poorly worded.

Hi Brent,

Let's not get into semantics but rather focus on the logic of the problem. Okay, I have put appropriate punctuation marks in the options. The error occured due to oversight. I was a bit exhausted after day's work and missed those marks. It's midnight in India & I am bit drowsy. Nevertheless your post was helpful.

I'm not trying to be difficult, but poorly-worded GMAT-style questions have the potential to confuse students who are trying to study for an already-difficult test.

Even with the edits, the question has issues. The biggest issue is that various values of x can make more than 1 answer correct. For example, if x = 0, then x� + 16 = 16, and the expressions in answer choices A, B, C and D all evaluate to be factors of x� + 16.

Conversely, if x = 0.1, then x� + 16 = 16.0001
What are the factors of 16.0001?

Another issue is to suggest that the correct answer is E - "Do not exist."
Does this mean that there are no factors of x� + 16?
If x is an integer, then we can be certain that 1 and (x� + 16?) are both factors.

To avoid ambiguity (and allow for only one correct answer), the question could read something like

Which if the following is equal to x^4 + 16 for all values of x?
(A) (x^2 + 4)(x^2 - 4)
(B) (x^2 + 4)(x^2 + 4)
(C) x(x^2 + 2)(x^4 + 4)
(D) (x^2 - 2)(x^2 + 2)
(E) none of the above


Answer: E

Cheers,
Brent