consider the polynomial.\ny = 3x^3 - 3x^2 - 126x\nwhat are the zeros of the given polynomial? select all…

Explanation:

Step1: Factor out the common factor

First, factor out (3x) from the polynomial (y = 3x^{3}-3x^{2}-126x). We get (y=3x(x^{2}-x - 42)).

Step2: Factor the quadratic expression

Factor the quadratic (x^{2}-x - 42). We need two numbers that multiply to (- 42) and add up to (-1). The numbers are (-7) and (6), so (x^{2}-x - 42=(x - 7)(x+6)). Then the factored - form of the polynomial is (y = 3x(x - 7)(x + 6)).

Step3: Find the zeros

Set (y = 0). Then (3x(x - 7)(x + 6)=0). Using the zero - product property, if (ab = 0), then either (a = 0) or (b = 0). If (3x=0), then (x = 0); if (x - 7=0), then (x = 7); if (x+6=0), then (x=-6).

Answer:

B. (-6), C. (0), E. (7)