What is x^5-2x^4-x^3-2x^2-20x+24<= 0 ?

The solution to x^5-2x^4-x^3-2x^2-20x+24<= 0 is x<=-2\lor 1<= x<= 3

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x^5-2x^4-x^3-2x^2-20x+24<= 0

x^{5} - 2 x^{4} - x^{3} - 2 x^{2} - 20 x + 24 \leq 0

x \leq - 2 or 1 \leq x \leq 3

Interval Notation

(- \infty, - 2] \cup [1, 3]

Solution steps

x^{5} - 2 x^{4} - x^{3} - 2 x^{2} - 20 x + 24 \leq 0

Factor

x^{5} - 2 x^{4} - x^{3} - 2 x^{2} - 20 x + 24 : (x - 1) (x + 2) (x - 3) (x^{2} + 4)

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

Identify the intervals

x \leq - 2 or 1 \leq x \leq 3

a (a - 2) \geq 2 (a + 6)

\frac{x}{( x - 1 )} > \frac{( x - 1 )}{x}

\frac{20 ( x - 2 )}{( x ^{2} + 1 )} < \frac{- 1}{2}

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

\frac{1}{( x ^{2} - 5 x + 6 )} \geq \frac{1}{2}

What is x^5-2x^4-x^3-2x^2-20x+24<= 0 ?
The solution to x^5-2x^4-x^3-2x^2-20x+24<= 0 is x<=-2\lor 1<= x<= 3