SOLUTION: what are the x-intercepts of h? h(x)=(3x^4-54x^2+96x-45)/(2x^3-x^2-32x+16)

Question 755192: what are the x-intercepts of h?
h(x)=(3x^4-54x^2+96x-45)/(2x^3-x^2-32x+16)
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

The x-intercepts are the values of x that make h(x)=0.
Those would be the values that make ,
as long as they do not also make
If there are rational zeros for , they would be integers that are factors of 15.
The possible zeros are -15, -5, -3, -1, 1, 3, 5, and 15.
The only ones of those that could be a zero of are -1 and 1, which are factors of 16, but neither is a zero of .

ZEROS OF :
is obviously one of the zeros, since

divides exactly by twice, and we find that

Then, is easy to factor as

So the full factorization of is

So the x-intercepts of h(x), which are zeros of h(x) and of are:
, , and
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