Graph the polynomial p(x)=-x^3(x+1)^2

Question

Labeling all intercepts.

Answer 1

p(x) = x³(x+1)²

p(x) = x³(x+1)(x+1)

 

To find the x-intercepts, we set p(x) equal to zero.

 

p(x) = 0

x³(x+1)(x+1)=0

 

x³ = 0          or      x = 0

x+1=0         or      x = -1

 

The x-intercepts are (0,0) and (-1,0).

 

 

To find the y-intercepts, we evaluate p(x) when x=0.

 

p(0) = 0³(0+1)²

p(0) = 0

 

The y-intercept is (0,0).