How do you find all the zeros of #f(x) = x^3 - 8x^2 - x + 8#?
1 Answer
Jul 2, 2016
Factor by grouping to find zeros:
#x=1# ,#x=-1# ,#x=8#
Explanation:
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:
