How do you find all the zeros of f(x)=x3+2x2−9x−18?

1 Answer
George C.
Mar 13, 2016

Factor by grouping and using the difference of squares identity to find zeros:

x=3, x=−3, x=−2

Explanation:

The difference of squares identity can be written:

a2−b2=(a−b)(a+b)

We use this with a=x and b=3 below, but first factor by grouping:

f(x)=x3+2x2−9x−18

=(x3+2x2)−(9x+18)

=x2(x+2)−9(x+2)

=(x2−9)(x+2)

=(x2−32)(x+2)

=(x−3)(x+3)(x+2)

Hence zeros:

x=3, x=−3 and x=−2

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