x^3 + 5x^2 - 4x - 20 <= 0
x^2(x + 5) - 4(x + 5) <= 0
(x^2 - 4)(x + 5) <= 0
(x + 2)(x - 2)(x + 5) <= 0
x = (-5, -2, 2)
check on a number line
pick any number greater than 2
3
3^3 + 5 * 3^2 - 4x - 20 <= 0
40 <= 0
false
no number greater than 2 is a solution
check any number less than -5
(-6)^3 + 5 * (-6)^2 - 4 * -6 - 20 <= 0
-32 <= 0
true
all numbers less than -5 are solutions
x <= -5
check between -5 and -2
(-4)^3 + 5 * (-4)^2 - 4 * -4 - 20 <= 0
12 <= 0
no numbers between -5 and -2 are solutions
check between -2 and 2
0^3 + 5 * 0^2 - 4 * 0 - 20 <= 0
-20 <= 0
all numbers between -2 and 2 are solutions
-2 <= x <= 2
x³+5x²-4x-20=x²(x+5)-4(x+5)
=(x²-4)(x+5)â¤0âxâ¤-5 & -2â¤xâ¤2.
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Verified answer
x^3 + 5x^2 - 4x - 20 <= 0
x^2(x + 5) - 4(x + 5) <= 0
(x^2 - 4)(x + 5) <= 0
(x + 2)(x - 2)(x + 5) <= 0
x = (-5, -2, 2)
check on a number line
pick any number greater than 2
3
3^3 + 5 * 3^2 - 4x - 20 <= 0
40 <= 0
false
no number greater than 2 is a solution
check any number less than -5
(-6)^3 + 5 * (-6)^2 - 4 * -6 - 20 <= 0
-32 <= 0
true
all numbers less than -5 are solutions
x <= -5
check between -5 and -2
(-4)^3 + 5 * (-4)^2 - 4 * -4 - 20 <= 0
12 <= 0
no numbers between -5 and -2 are solutions
check between -2 and 2
0^3 + 5 * 0^2 - 4 * 0 - 20 <= 0
-20 <= 0
all numbers between -2 and 2 are solutions
-2 <= x <= 2
x <= -5
-2 <= x <= 2
x³+5x²-4x-20=x²(x+5)-4(x+5)
=(x²-4)(x+5)â¤0âxâ¤-5 & -2â¤xâ¤2.