find all zeros of the polynomial function
f(x)=x^4-6x^3+7x^2+6x-8

Question

find all zeros of the polynomial function
f(x)=x^4-6x^3+7x^2+6x-8

anonymous · Answer

i am not completely clueless i have an idea of it but im stuck on a step:S

campbell_st · Answer

the factors of the constant term are  call them p

$$\pm 1, \pm 2, \pm 4, \pm 8$$

 the factors of the leading term are call them q

$$\pm 1$$

so the rational factors are p/q

so try x = -1 

$$f(-1) = (-1)^4 - 6(-1)^3 + 7(-1)^2 + 6(-1) - 8$$

f(-1) = 0 so then (x + 1)

now try 

x = 1

f(1) = 0 so ( x - 1) is a factor 

this means x^2 -1 is also a factor 

 so do some polynomial division 

|dw:1358719209859:dw|

this should result in a quadratic factor.. which could then be factorised to find the linear factors and hence all the zeros.