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Answer 1 · 2017-06-13T21:19:34

#x^4-10x^3+20x^2+40x-96#

If we already have the zeros they original came from solving for x:
This is what we have right now #x=-2,2,4,6#
So we work our way backwards:

#x=-2# You add two to both sides
#x+2=cancel(-2+2)#
#color(blue)(x+2)# This is one factor

#x=2# Subtract two from both sides
#x-2=cancel(2-2)#
#color(blue)(x-2)# Another factor

#x=4# Subtract four from both sides
#x-4=cancel(4-4)#
#color(blue)(x-4)# Third factor

#x=6# Subtract six from both sides
#x-6=cancel(6-6)#
#color(blue)(x-6)# Final factor

Now that we know this information we can now multiply out our factors of:

#(x+2)(x-2)(x-4)(x-6)#

#(x^2-4)(x-4)(x-6)#

#(x^3-4x^2-4x+16)(x-6)#

#x^4-6x^3-4x^3+24x^2-4x^2+24x+16x-96#

Simplify:

#x^4-10x^3+20x^2+40x-96#