What is (x-1)(x-2)(x-4)(x-5)>40 ?

The solution to (x-1)(x-2)(x-4)(x-5)>40 is x 6

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(x-1)(x-2)(x-4)(x-5)>40

(x - 1) (x - 2) (x - 4) (x - 5) > 40

x < 0 or x > 6

Interval Notation

(- \infty, 0) \cup (6, \infty)

Solution steps

(x - 1) (x - 2) (x - 4) (x - 5) > 40

Rewrite in standard form

x^{4} - 12 x^{3} + 49 x^{2} - 78 x > 0

Factor

x^{4} - 12 x^{3} + 49 x^{2} - 78 x : x (x - 6) (x^{2} - 6 x + 13)

x (x - 6) (x^{2} - 6 x + 13) > 0

Identify the intervals

x < 0 or x > 6

(x - 2) (x - 4) (x - 6) > 0

\frac{( ( x - 1 ) \cdot ( x + 2 ) ^{2} )}{( - 1 - x )} < 0

\frac{1}{x ^{3}} > - 27

\frac{( 2 x - 4 )}{( 3 - x )} \geq 1

\frac{( ( x + 2 ) ( x ^{2} - 2 x + 1 ) )}{( 4 + 3 x - x ^{2} )} \geq 0

What is (x-1)(x-2)(x-4)(x-5)>40 ?
The solution to (x-1)(x-2)(x-4)(x-5)>40 is x<0\lor x>6