Thread: factoring a higher order trinomial (odd)

Hi - I am stuck on a question that requires me to find the 2nd point of intersection between a power function (x^3) and the tangent of the function at a given point (1/2, 1/8), which I determined to be y=3/4x - 1/4

I have combined the two equations and created a 3rd order trinomial 0=x^3 -3/4x +1/4. My problem is that I forget how to factor a trinomial with an odd power. Any help would be appreciated.

Thanks in advance.

Honestly, its really hard to remember the cubic one,

but if you need it solved, click the link.

0=x^3 -3/4x +1/4 - Wolfram|Alpha

Thanks for the link - I see it being of value in the future. However, I really want to figure this one out.

But you know that this line is a tangent to the cubic so you have a repeated root at x=1/2.


Now you just need to find the other factor.

Thanks a tutor. I understand that the first point of intersection is 1/2 and that the tangent will intersect at a second point, which can be determined by figuring out the second factor, but that is exactly my problem. I cannot remember how to determine the other factor for a cubic trinomial that cannot be simplified into a quadratic. I believe mine cannot 0=x^3 -(3/4)x + 1/4.

Honestly, it has been a while since I studied these earlier concepts and I used to struggle with factoring. Is there a different theorem or method that can be applied?

0=x^3 -(3/4)x + 1/4

is a zero, use synthetic division ...

Code:

[1/2].........1.........0........-3/4..........1/4
.......................1/2........1/4..........-1/4
-------------------------------------------------------
..............1........1/2.......-1/2............0

I was thinking



It's pretty clear that it has to be

I think I'm lazy.

Thanks guys. You both have helped a lot.