bionomial has 2 terms trinomial has 3 terms polynomial has more than 1 terms, it has a countable number of terms, the exponents of the placeholders have to be whole numbers
so bionimal could be x+2 or x³-2 trinomal could be x²+2x-3
polynomail could be all of the above, example 2x²-3x³+24x⁴-4+x