What is (x-2)^3(x-4)^2(x-10)17>0 ?

The solution to (x-2)^3(x-4)^2(x-10)17>0 is x 10

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(x-2)^3(x-4)^2(x-10)17>0

(x - 2)^{3} (x - 4)^{2} (x - 10) 17 > 0

x < 2 or x > 10

Interval Notation

(- \infty, 2) \cup (10, \infty)

Solution steps

(x - 2)^{3} (x - 4)^{2} (x - 10) \cdot 17 > 0

Rewrite in standard form

x^{6} - 24 x^{5} + 216 x^{4} - 960 x^{3} + 2256 x^{2} - 2688 x + 1280 > 0

Factor

x^{6} - 24 x^{5} + 216 x^{4} - 960 x^{3} + 2256 x^{2} - 2688 x + 1280 : (x - 2)^{3} (x - 4)^{2} (x - 10)

(x - 2)^{3} (x - 4)^{2} (x - 10) > 0

Identify the intervals

x < 2 or x > 10

x (x + 3) < 0

\frac{3 x ( x - 1 )}{5 x} \geq 0

x^{4} + 6 x \leq 6 x^{3} + x^{2}

(x - 1) (x - 5) > 4

\frac{x - 4}{x + 2} < 0

What is (x-2)^3(x-4)^2(x-10)17>0 ?
The solution to (x-2)^3(x-4)^2(x-10)17>0 is x<2\lor x>10