Question

Polynomial p has zeros when x=0, x=−1/6 , and x=−3. What could be the equation of p?

a) p(x)=x(x+1/6)(x+3)
b) p(x)=(x−0)(x+1/6)(x+3)
c) p(x)=(x+0)(x+1/6)(x+3)
d) p(x)=x(x−1/6)(x−3)

Answer 1

The equation of p is p(x) = x(x+1/6)(x+3).

Step-by-step explanation:

The equation has zeros at x=0, x=-1/6, and x=-3. In order to find the equation of p, we can use these zeros to write the factors of the polynomial. Since x=0 is a zero, one of the factors will be x. Since x=-1/6 is a zero, one of the factors will be (x+1/6). And since x=-3 is a zero, one of the factors will be (x+3). Multiplying these factors together, we get the equation of p as: p(x) = x(x+1/6)(x+3). Therefore, the correct answer is (a).