If k is a constant such that x-2 and x+2 are factors of the polynomial 100x^2+k what is the value of k?

Question

lgbasallote · Answer

do you know the remainder theorem? or no?

anonymous · Answer

no..

lgbasallote · Answer

what about synthetic division/polynomial division?

anonymous · Answer

I feel like I've learned about them, but I don't remember how to do them

lgbasallote · Answer

what about difference of two squares? i'm sure you know it?

anonymous · Answer

Maybe if you just explain how to do the problem out it might refresh my memory...

lgbasallote · Answer

well....i don't know if this is how your teacher would like this problem to be solved....but here goes..

lgbasallote · Answer

your problem says x-2 and x+2 are factors, yes?

lgbasallote · Answer

so that means you can write it like this

(x-2)(x+2)

agree?

anonymous · Answer

yesss

lgbasallote · Answer

so then...if you multiply (x-2)(x+2) what do you get?

anonymous · Answer

is it x^2 - 4?

lgbasallote · Answer

yes!

lgbasallote · Answer

so then

compare x^2 - 4 to 100x^2 - k

lgbasallote · Answer

what can you do to x^2 to make it look like 100x^2?

anonymous · Answer

I mean the only difference I can see is the 100...

lgbasallote · Answer

sorry i was away...

lgbasallote · Answer

so what should you do to x^2 to make it look like 100x^2?