Determine whether the following polynomial is a perfect square trinomial: x^3 + 8x + 16
Yes or No

Question

anonymous · Answer

lol but I'm 50% sure the answer is yes

anonymous · Answer

Lol what? xD

anonymous · Answer

@phi

kirbykirby · Answer

No, not if you have a degree-3 polynomial.
Perfect square trinomial has the form:
$(x+a)^2 = x^2+2ax+a^2$ 
or
$(x-a)^2=x^2-2ax+a^2$

anonymous · Answer

i think its no but how to find the sqrt of $x^3$

phi · Answer

if you have x^3  then it won't be

anonymous · Answer

but how do you know

phi · Answer

the square root of x^3  is $ x^{\frac{3}{2}} $
which is not "perfect"  i.e.  x

anonymous · Answer

yes keep going on

kirbykirby · Answer

You need to somehow get a form (smtg + smtg)^2 when you factor it

phi · Answer

they are assuming the square root will be a binomial of the form  (x+a)
where a is a number.

or, if we relax the requirement and allow 
$$ (x^n + a) $$
where n is an integer, we would get
$$ (x^n + a)^2 = x^{2n}+ 2ax^n +a^2 $$
and the highest exponent is even  (2n will be an even number)

the only way to get an exponent of 3 is to start with 3/2
and 3/2 is not integer....  
and we insist on "simple"  (x+a)  or maybe (x^n +a) as the starting binomial... otherwise it's not perfect.

anonymous · Answer

ohhhhhhhhhhh, of course @phi  $x^3≠~perfect$

anonymous · Answer

thx @phi so the answer is a no

phi · Answer

definitely NO