Three students each propose a polynomial with zeroes 0, 0 and 3 (a double zero at 0).
Which degree-3 polynomial matches this exactly?

Question

Three students each propose a polynomial with zeroes 0, 0 and 3 (a double zero at 0). Which degree-3 polynomial matches this exactly?

Accepted Answer

x^2(x - 3). A double zero at 0 contributes factor x^2; a zero at 3 contributes (x - 3). So p(x) = x^2(x - 3), degree 3.

Step-by-Step Solution