Answer:
f(x) = x³ -6x² -x +30
Step-by-step explanation:
You want the simplest polynomial with zeros 5, -2, 3.
Factor
Each zero at p corresponds to a factor of (x -p) of the polynomial. For the given zeros, the factored form of the polynomial is ...
f(x) = (x -5)(x +2)(x -3)
When this is expanded, the function is ...
f(x) = x³ -6x² -x +30
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Additional comment
The expansion makes use of the distributive property. We find it convenient to save the (x+2) factor for last to minimize the number of minus signs we must deal with.
f(x) = (x +2)(x -3)(x -5) = (x +2)(x² -8x +15)
= x³ -8x² +15x +2x² -16x +30
= x³ -6x² -x +30
