Thank you for the opportunity to help you with your question!

Thank you for the opportunity to help you with your question!

x^3 + 5x^2 >or equal to 4x + 20

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

Please let me know if you need any clarification. I'm always happy to answer your questions.
Please let me know if you need any clarification. I'm always happy to answer your questions.