The polynomial p_1 (x) = (x - 1)^6 has the value zero at x = 1 and is positive elsewhere. The expanded form of the polynomial p_2 (x) = x^6 - 6x^5 + 15x^4 - 20x^3 + 15x^2 - 6x + 1, is mathematically equivalent. Plot p_1 (x) and p_2(x) for 101 equally spaced points in the interval [0.995, 1.005]. Explain the plots. (you should evaluate the polynomial p_2(x) by Horner's rule)