The Polynomial of degree 3 with three distinct real zeros and a positive leading coefficient is P(x) = x³ - x
Let the distinct real zeros of the required polynomial be 0, 1 and -1.
The equivalent factors will be x(x-1)(x+1)
To get the required polynomial, we will take the product of the factors as shown:
P(x) = x(x-1)(x+1)
P(x) = (x+1)(x-1)x
P(x) = x(x²-1)
P(x) = x³ - x
Hence the Polynomial of degree 3 with three distinct real zeros and a positive leading coefficient is P(x) = x³ - x
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