# Thread: Polynomials and Solving Inequalities...

1. ## Polynomials and Solving Inequalities...

I need help getting the answers for these 2 questions!
I want to see if i did them right... (because i dont have an answer sheet)

1) Solve 12x^3 - 16x^2 + 7x -1
Let f(x) = 12x^3 - 16x^2 + 7x -1

2) Solve the inequality:
3x / (x^2 -4) < -1

*note: where the "<" is, its supposed to be less than/equal to. (i just cant find a key for it :P )

Thanks again!

2. 1. solve for what? zeros of the function?

2. inequality problem ...

3x/(x^2 - 4) < -1

3x/(x^2 - 4) + 1 < 0

3x/(x^2 - 4) + (x^2 - 4)/(x^2 - 4) < 0

(x^2 + 3x - 4)/(x^2 - 4) < 0

[(x+4)(x-1)]/[(x+2)(x-2)] < 0

critical x-values are where the left side = 0 or is undefined.

x = -4, x = 1, x = -2, and x = 2

mark these 4 x-values on a number line ... this breaks up the x-values into 5 regions. test any x-value in each region in the above inequality.
if the inequality is true, then all values of x in that region make the inequality true ... if false, exclude that region from the solution set.

don't forget that x = -4 and x = 1 will be included in the solution set because they make the expression = 0.

3. thanks!

and for #1, , yes, zeros of the function

4. did you attempt the rational root theorem for #1 ?

5. lol dont worry, i checked with my teacher today, and i did the questions correctly!

thanks for the help on #2! it really helped me ALOT!