Solve this inequality. \[(x-4)^2(x+3) \ge 0\]Write your answer in interval notation.

Answer 1

Solving: (x-4)²(x+3) >= 0

Boundary points: (x-4)²(x+3) = 0 gives x = 4 or x = -3

The boundary points split the x axis into 3 intervals:

Interval Sign

(-oo,-3) -

(-3, 4) +

(4, oo) +

The solution is all intervals with positive sign and including the boundary points where the expression equals zero: (-3, 4), (4, oo) including the points -3 and 4, so the combined solution is [-3, oo).