I am curious why the answer is not D for this

Isn’t the square root of a binomial equal to it’s absolute value?

Thanks!

I am curious why the answer is not D for this

Isn’t the square root of a binomial equal to it’s absolute value?

Thanks!

Well,

- it’s not a binomial, rather a trinomial (three terms)
- Quantity A is not a quadratic, it’s a quartic (degree 4 polynomial)
- Can either of the two quantities be negative?

Thanks for your response. My thought process was below. Is that not correct? Also, I realized I forgot to write the x^2 in the 6x^2. Apologies for that. Thank you for your help!

I am wondering if the issue might be I can’t convert x^4 +6x^2 + 9 to (x^2+3) underneath a square root? Is that the issue?

It is technically correct to say that

\sqrt{x^4 + 6x + 9} = |x^2 + 3|

However, the absolute value only kicks in if the term inside it could be negative. x^2 + 3 can be no less than 3. Hence,

|x^2 + 3| = x^2 + 3

Conversely, it is **not** true that

|x + 3| = x + 3

Can you see why?

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