Solve the inequality
x^3 + 5x^2 >or equal to 4x + 20
Write your answer as an interval or union of intervals.
Please note that the sign is supposed to have a line under it making it 'or equal to.'
Thank you for the opportunity to help you with your question!
we can first ignore the sign and do it this way;
x^3 + 5x^2 = 4x + 20
x^3 + 5x^2 - 4x - 20 = 0 solve for x by factoring by grouping: (x^3 + 5x^2) - (4x + 20) = 0 factor out common term x^2(x+5) - 4(x+5) = 0 Factor out the (x+5) (x+5)(x^2-4) = 0 the x^2-4 is a difference of two squares and thus can be factored more (x+5)(x+2)(x-2) = 0 set each term to zero and solve for x x+5 = 0 OR x+2 = 0 OR x-2 = 0 x = -5 OR x = -2 OR x = 2
as interval notation: (-inf, -5] U [-2,2]
-2 >= x >= 2
I typed it in exactly and it stated it as incorrect
Sorry for that dear! Let have a check on it.
(X+2)(X-2)(X+5)=0X=-2 SOLUTIONX=2 "X=-5 "
are your brackets and paratheneses right?
Sure..x should be greater or equal to both 2 and -5
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