Thread: Please help me with 4 quick polynomials

I just can't figure out these 4...Would be very happy if someone could help me out
Solve the equations:
1) (2x^3 -3x^2 -3x+2) / (x+1) < 0

2) (x^3 -2x^2 -3x) > 0

Solve the divisions
3) (2x^3 +9x^2 -7x -4) : (x^2 +2x -3)

4) x^4 : (x^2 - 4)
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Originally Posted by pizdac

I just can't figure out these 4...Would be very happy if someone could help me out
Solve the equations:
1) (2x^3 -3x^2 -3x+2) / (x+1) < 0

Do the division

.

Now as the coefficient of is positive between the roots
of the quadratic on the right (if these are real). The roots are and . So:

, when

RonL

Originally Posted by pizdac

2) (x^3 -2x^2 -3x) > 0

The LHS of this inequality is a cubic, it has either three real roots, or but
a single root. Also as the cubic is positive.

So if there is only a single root the cubic is to the right
of the root.

If there are three roots it is to the right of the greatest root,
and again between the other two roots.

(Sketch a cubic and you will see why this is so).

As there is no constant term in the cubic we can factor it:

,

and so we can find the other roots using the quadratic formula.

RonL

Problem 4

Problem 2)

Factor,

Once more,
.
Now find the zero,

Now observe each interval.




Just pick points and see if the polynomial is positive or negative.
Doing that we find that
This is Negative (Wrong)
This is Positive (Correct)
This is Negative (Wrong)
This is Positive (Correct)
Answer:

Or another way of writing .

Thank you very much