EQUAÇÕES POLINOMIAIS - Fuvest 2019

Solution to the question whose statement is: "(Fuvest − 2019) Consider the sketch of the graph of the polynomial P(x) = (x − 1)²(x + 2)³(x − 2) and indicate the FALSE statement. (A) P(x) is a polynomial of degree 6. (B) P(x) is positive for all x ∈ [0, +∞). (C) P(x) does not change sign in the interval (−1, 1) of its domain. (D) P(x) does not have imaginary (non-real) roots. (E) The graph of P(x) is tangent to the x-axis at x = 1."