1. ## Polynomial inequality

Solve the poynomial inequality. Write the answer in interval notation. Could you show your work since I don't get these. Thanks
(T-7)(T+1) is less than 0.

x^3 + 36 is greater than to 4x^2 + 9x

2. Hello,

Originally Posted by rowdy3
Solve the poynomial inequality. Write the answer in interval notation. Could you show your work since I don't get these. Thanks
(T-7)(T+1) is less than 0.
A product is negative if the two factors are of different sign.

-> T-7>0 and T+1<0
Or T-7<0 and T+1>0

x^3 + 36 is greater than to 4x^2 + 9x
For this one,

x^3+36>4x^2+9x

<=> (x^3-9x)+(36-4x^2)>0

<=> x(x²-9)+4(9-x²)>0

<=> (x²-9)(x-4)>0

A product is positive if its factors are of the same sign.

-> x²-9>0 and x-4>0
Or x²-9<0 and x-4<0

3. x^2 + 2x + 1 less than 0
This is what I did.
X^2 + 2x + 1 less than 0.
-1 -1
x^2 + 2x less than -1
Divide by x.
x + 2 less than -1
No solution.

4. Originally Posted by rowdy3
x^2 + 2x + 1 less than 0
This is what I did.
X^2 + 2x + 1 less than 0.
-1 -1
x^2 + 2x less than -1
Divide by x.
x + 2 less than -1
No solution.
Hehe, don't bother ^^

x²+2x+1=(x+1)²

Can a squared number be negative ?

5. Ouuuh, I missed a mistake :

Divide by x.
x + 2 less than -1
Do you know why, in my first post, I only said that there were two solutions ?
Because you don't know if x is positive or negative.

If it's positive, it keeps the sign of the inequality.
If it's negative, < will become >.

An example :

6>4
If you divide both sides by -2, is it -3>-2 or -3<-2 ?