1. ## function

The polynomial P(x) =x4-4x3+hx2-6x+2 has a factor in the form (x-m)2, find the values of m and h.

P(x) =x4-4x3+hx2-6x+2
P(m) = 0
m4-4m3+hm2-6m+2=0
P’(x) =4x3-12x2+2hx-6
P’(m)=4m3-12m2+2hm-6=0
-m5+4m4+6m2-2m=-2m5+6m4+3m2
m5-2m4+3m2-2m=0
÷m, m4-2m3+3m-2=0
Try m=1, (1)4-2(1)3+3(1)-2=0
Hence, m=1, h=7

I think there is something wrong in my solution, can anyone help?

2. ## Re: function

Hey Trefoil2727.

You should try dividing P(x) by (x-m)^2 and note that your remainder must be 0. Once you have done this you will end up with a quadratic which you can find the roots for using the standard result.

3. ## Re: function

No, Trefoil2727, your answer, m= 1, h= 7, is exactly correct as you can see by modifying chiro's suggestion and dividing $x^4- 4x^3+ 7x- 6x+ 2$ by $(x- 1)^2$.

4. ## Re: function

but if I use chiro's suggestion, i would've 3 unknown(h, m and x) and i can't eliminate them..