What is x^4(x-1)^3(x+2)^2(x-5)(x+6)^2<0 ?

The solution to x^4(x-1)^3(x+2)^2(x-5)(x+6)^2<0 is 1<x<5

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x^4(x-1)^3(x+2)^2(x-5)(x+6)^2<0

x^{4} (x - 1)^{3} (x + 2)^{2} (x - 5) (x + 6)^{2} < 0

1 < x < 5

Interval Notation

(1, 5)

Solution steps

x^{4} (x - 1)^{3} (x + 2)^{2} (x - 5) (x + 6)^{2} < 0

Identify the intervals

1 < x < 5

\frac{( 3 x - 5 )}{( x ^{2} - 4 )} > 0

4 x - \frac{17}{x} - 4 + 10 x - \frac{3}{2} x - 3 > 8 x - \frac{30}{2} x - 7

(3 x + 3) (5 x - 3) > 0

\frac{( x - 3 )}{( x ^{2} + 9 x - 22 )} < 0

4 x^{2} - 4 x + 3 < 0

What is x^4(x-1)^3(x+2)^2(x-5)(x+6)^2<0 ?
The solution to x^4(x-1)^3(x+2)^2(x-5)(x+6)^2<0 is 1<x<5