How do you find all the zeros of #f(x) = x^3 + 2x^2 - 9x -18#?

Question

9387 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-13T00:31:02

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

#x=3#, #x=-3#, #x=-2#

The difference of squares identity can be written:

#a^2-b^2 = (a-b)(a+b)#

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

#f(x) = x^3+2x^2-9x-18#

#=(x^3+2x^2)-(9x+18)#

#=x^2(x+2)-9(x+2)#

#=(x^2-9)(x+2)#

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

#=(x-3)(x+3)(x+2)#

Hence zeros:

#x = 3#, #x = -3# and #x = -2#