If 4t^3-2t^2-8t+16 is divisible by t^2, then 4t^3-2t^2-8t+16 divided by t^2 must be an integer.
Start by dividing the expression by t^2. You can do this term by term to get:
4t-2-8/t+16/t^2. We need this to be an integer if the answer is yes, which essentially means t must be something that divides 8, and t^2 must be something that divides 16.
1. This is not helpful. It could be divisible if t=2 or 4. Or not divisible if t=anything else. INSUFFICIENT.
2. this tells us that t=2 because 2 is the only even prime number. As discussed above, this means the expression is, in fact, divisible by t^2. SUFFICIENT.
Is 4t^3-2t^2-8t+16 divisible by t^2 ?
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The only positive Prime number is 2lenagmat wrote:Is 4t^3-2t^2-8t+16 divisible by t^2 ?
1. t>1
2. t is an even prime number
A is B.
HenceB
