solve each polynomial inequality. Approximately to three decimal places if necessary?

(x + 4)(3x - 9) (x - 1) < 0

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  • 1 month ago

    Since this is already factored makes this easier.  If this were an equation we'd see that the roots are:

    x = -4, 1, 3 

    (3x - 9) can be factored further to 3(x - 3), then dividing both sides by 3 would get rid of the 3.

    We can use this information to check values between the roots and see which ones result in a value less than zero (aka, negative numbers):

    if x > 3 we have positive times positive times positive, which is positive.

    if 1 < x < 3 we have positive times positive times negative, which is negative.

    if -4 < x < 1 we have positive times negative times negative, which is positive.

    if x < -4 we have negative times negative times negative, which is negative.

    So the solution to your inequality is:

    x < -4 and 1 < x < 3

    or:

    (-∞, -4) U (1, 3)

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