How do you find all zeros of #f(x)=x^3-4x^2-25x+100#?

1 Answer
Jan 7, 2017

Answer:

#x=5#, #x=-5# or #x=4#

Explanation:

Note that the ratio of the first and second terms is the same as that of the third and fourth terms, so this cubic factors by grouping and we find:

#0 = x^3-4x^2-25x+100#

#color(white)(0) = (x^3-4x^2)-(25x-100)#

#color(white)(0) = x^2(x-4)-25(x-4)#

#color(white)(0) = (x^2-25)(x-4)#

#color(white)(0) = (x^2-5^2)(x-4)#

#color(white)(0) = (x-5)(x+5)(x-4)#

Hence #x=5#, #x=-5# or #x=4#