Question 36950
Hello!
An x-intercept is a value of x that makes y equal to zero.

In your case, we have:
{{{y=x^3(x+2)(3x-1)}}}

Clearly, since they are all multiplied, if any of the terms {{{x^3}}}, {{{x+2}}} or {{{3x - 1}}} is equal to zero, then y will be equal to zero. So let's find the x-intercepts:

{{{x^3 = 0}}}
This term is equal to 0 when x = 0. So one of the x-intercepts is x = 0


{{{x+2}}}
This term is equal to zero if x = -2. So another x-intercept is x= -2


{{{3x - 1}}}
This term is equal to zero if x = 1/3. So another x-intercept is x = 1/3.

So the three x-intercepts for this equation are: 0, -2, 1/3


I hope this helps!
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