There are two types of polynomials, those that have zeros and those that don't. If you think about it graphically, the polynomial must touch the "x" axis to have a zero. If you are finding polynomials graphically, you can easily make the polynomial have zeros or not based on whether you make it intersect with the "x" axis. To do this without the graph is a little more complicated but still only takes a few easy steps.
Instructions
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1
Pick the zeros you wish to have. If you want to have 3 zeros, pick three numbers.
For example, 3 and -5
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2
Create the factors for the polynomial by putting the numbers you selected in the following format: (x- {first number}) * (x- {second number})* ......and so on
For our example, (x-3) * (x+5)
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3
Multiply the factors.
For our example, x^2 + 5x - 3x - 15
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4
Add the answer to get your final polynomial.
For our example, x^2 + 2x - 15