How do you find all the zeros of f(x)=x3−8x2−x+8?

1 Answer
George C.
Jul 2, 2016

Factor by grouping to find zeros:

x=1, x=−1, x=8

Explanation:

f(x)=x3−8x2−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:

x3−8x2−x+8

=(x3−8x2)−(x−8)

=x2(x−8)−1(x−8)

=(x2−1)(x−8)

=(x−1)(x+1)(x−8)

Hence zeros: x=1, x=−1, x=8

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