Need help understanding this..

For the polynomial f(x) =2x^4 - 8x^2 +7x - 25 ,x -- - oo , f(x) -- oo
Is this true or false?
and why?

Question

Need help understanding this..

For the polynomial f(x) =2x^4 - 8x^2 +7x - 25 ,x --> - oo , f(x) --> oo
Is this true or false?
and why?

anonymous · Answer

polynomial has even degree (it is 4) and the leading coefficient is positive (it is 2) as as $x\to -\infty$ you know $f(x)\to \infty$

anonymous · Answer

forget all the lower terms, they are not important here
think about a large negative number like $-1,000,000$ and imagine what you get when you compute 
$$2(-1,000,000)^2$$

shamil98 · Answer

I would get a large positive number..

wolfe8 · Answer

It means that since your powers are even numbers, you will only end up adding positive number. no negatives since all negative values for x are made positive, right @satellite73 ?

shamil98 · Answer

So its true, because the polynomial has an even degree?... and the leading coefficient is positive?

shamil98 · Answer

Does that mean if polynomial has a leading coefficient that is negative  this would not be true?

wolfe8 · Answer

Eh ask Satellite from here. I'm not even sure myself

shamil98 · Answer

@satellite73 am i correct? thanks, though, wolfe.