How do you factor given that #f(-14)=0# and #f(x)=x^3+11x^2-150x-1512#?

1 Answer
KillerBunny
Oct 5, 2016

#(x-12)(x+9)(x+14)#

Explanation:

When you know that #f(c)=0# for some value #c#, you knot that #f(x)# has a factor #(x-c)#. So, you can divide #x^3+11x^2-150x-1512# by #(x+14)# via long division, or whatever method you prefer, and obtain

#(x^3+11x^2-150x-1512)/(x+14) = x^2-3 x-108#

which means

#(x^2-3 x-108)(x+14) = x^3+11x^2-150x-1512#

Again, #x^2-3 x-108# has solutions #12# and #-9#, which means that it can be written as #(x-12)(x+9)#

Thus, we can write

#x^3+11x^2-150x-1512 = (x^2-3 x-108)(x+14) = (x-12)(x+9)(x+14)#

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