I need help solving this in interval notation

To solve x^2(x-3)(x-9)^5>0, we need to look at each factor.

X^2 will always be positive (even exponents give positive results).

(x-3) can be positive or negative.

(x-9)^5 can be positive or negative.

For the entire expression to be positive, either:

x^2 is positive AND (x-3) is positive AND (x-9)^5 is positive (+++)

or x^2 is positive AND (x-3) is negative AND (x-9)^5 is negative (+--).

This give us two scenarios:

A) x^2>0; x>0

& x-3>0; x>3

& (x-9)^5>0; x-9>0; x>9

x>0 & x>3 & x>9 : x>9 : (9,infinity)

B) x^2>0; x>0

& x-3<0; x<3

& (x-9)^5<0; x-9<0; x<9

x>0 & x<3 & x<9 : 0<x<3 (0,3)

Combining A and B; x>9 or 0<x<3; (9,infinity)U(0,3)

## Comments

I am not sure if the ^5 covers both (x-3) AND (x-9) or if it just covers the (x-9). If it encompasses both, you need to put another pair of parenthesis around the two like this ((x-3)(x-9))^5 That information would be needed in order to answer the question correctly.

It covers just the (x-9).