(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The problem states:

Consider the function f(x)=x^{4}-8x^{3}+2x^{2}+80x-75

a) Verify that x-1 and x-5 are factors

b) Find the remaining factors of f(x)

c) List all real zeros

2. Relevant equations

I did synthetic division to prove that 1 and 5 are factors, yet I'm having trouble figuring out how to get the remaining zeros.

3. The attempt at a solution

I tried splitting up the equation and factoring out from both sides and got:

x^{3}(x-8)+2x(x-40)-75

And I just got lost from here. I'm blanking on how to find the zeros besides just choosing a bunch of numbers and doing synthetic division a bunch of times.

Thanks for any help!

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# Homework Help: Finding zeros of a quartic function

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