we want to find the zeros of this polynomial:

p(x)=(x-1)(x+3)(2x+1)

plot all the zeros (x-intercepts) of the polynomial in the interactive graph.

Step-by-step explanation:

To find the zeros of this polynomial, set the polynomial equal to zero, and then set each of the factors equal to zero separately.  Solve each equation for x:

x  - 1 = 0 yields x = 1.     The x-intercept is (1, 0).

x + 3 = 0 yields x = -3.   The x-intercept is (-3, 0).

2x + 1 = 0 yields x = -1/2   The x-intercept is (-1/2, 0)

(- 3, 0), (- 1/2, 0), (1, 0)

Step-by-step explanation:

p(x)=(x-1)(x+3)(2x+1)

Plug p(x) = 0

Therefore,

(x-1)(x+3)(2x+1) = 0

x - 1 = 0 or x + 3 = 0 or 2x + 1 = 0

x = 1 or x = - 3 or x = - 1/2

Hence, (- 3, 0), (- 1/2, 0), (1, 0) are zeroes of the given polynomial