Solve the higher degree inequalities.

x^2(x+5)^3
≤0
(3−x)(x+3)^2

The solution of the inequality is .

Step-by-step explanation:

The given inequality is

Equate each factor of numerator and denominator equal to 0.

The points -5,-3, 0 and 3, divides the number line in five parts. The intervals are

The zero points are -5,-3, 0 and 3 with multiplicity 3, 2, 2 and 1 respectively.

According to the Wavy Curve Method the statement (True or false) change according to the multiplicity of the zeros point.

If the multiplicity is even then statement remains same for next interval and if  the multiplicity is odd then statement changes.

Put x=-4

This statement is false.

From the given number line we can say the solution of the inequality is

Therefore the solution of the inequality is .

step-by-step explanation:

i have done this all on a piece of paper but idk how to put it on here cuz it needs to be drawn