# How do you create a polynomial p which has degree 4, as #x->oo, p(x)->-oo#, p has exactly three x intercepts (-6,0), (1,0) and (117,0), the graph of #y=p(x)# crosses through the x axis at (1,0)?

##### 1 Answer

Apr 2, 2017

There are basically two possibilities:

#{ (p(x) = k(x+6)^2(x-1)(x-117)), (p(x) = k(x+6)(x-1)(x-117)^2) :}#

with

#### Explanation:

The leading coefficient of

It must have linear factors

As there are only three

Also since

So there are basically two possibilities:

#{ (p(x) = k(x+6)^2(x-1)(x-117)), (p(x) = k(x+6)(x-1)(x-117)^2) :}#

with