# math (double checking)

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I've posted this question before but I forgot to say that I was dealing with polynomial inequalities (not sure if that makes a difference)

The question is: Solve the following polynomial inequalities. (9 marks)

4x - 5 ≤ 2(x - 7)
x^3 - 5x^2 + 2x ≥ -8
2(x^3 - 2x^2 + 3) < x(x - 1)(x + 1)

The answer Reiny previously gave me is the following and I just wanted to double check it:

1.

4x - 5 ≤ 2x - 14
-x ≤ -9
x ≥ 9

2.

x^3 - 5x^2 + 2x + 8 ≥ 0
(x-4)(x-2)(x+1) ≥ 0
critical values are x = 4,2, and -1

the graph of f(x) = (x-4)(x-2)(x+1)
lies above the x-axis between -1 and 2, and values > 4
so -1 ≤ x ≤ 2 OR x ≥ 4

3.

2x^3 - 4x^2 + 6 < x^3 - x
x^3 - 4x^2 + x + 6 < 0
This expression also factors,
hint: (x+1) is a factor

I will let you finish it, let me know what you got

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