How do you find all the zeros of #f(x) = x^3 - 8x^2 - x + 8#?

1 Answer
Jul 2, 2016

Answer:

Factor by grouping to find zeros:

#x=1#, #x=-1#, #x=8#

Explanation:

#f(x) = x^3-8x^2-x+8#

Notice that the ratio of the first and second terms is the same as that between the third and fourth. So this cubic factors by grouping:

#x^3-8x^2-x+8#

#=(x^3-8x^2)-(x-8)#

#=x^2(x-8)-1(x-8)#

#=(x^2-1)(x-8)#

#=(x-1)(x+1)(x-8)#

Hence zeros: #x=1#, #x=-1#, #x=8#