How do you factor given that #f(10)=0# and #f(x)=x^3-12x^2+12x+80#?

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Answer 1 · 2016-12-19T08:13:23

#f(x)=x^3-12x^2+12x+80=(x-10)(x+2)(x-4)#

As #f(x)=x^3-12x^2+12x+80# and #f(10)=0#

#(x-10)# is a factor of #f(x)=x^3-12x^2+12x+80#

Now dividing #f(x)=x^3-12x^2+12x+80# by (x-10)#, we can get a quadratic polynomial which can be factorized further by splitting the middle term.

#f(x)=x^3-12x^2+12x+80#

= #x^2(x-10)-2x(x-10)-8(x-10)#

= #(x-10)(x^2-2x-8)#

= #(x-10)(x^2-4x+2x-8)#

= #(x-10)(x(x-4)+2(x-4))#

= #(x-10)(x+2)(x-4)#