Is x-1 a factor of #x^3+5x^2+2x-8#?

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Answer 1 · 2016-09-26T07:46:44

#f(1) = 0#
#(x-1)# is a factor

Call the given expression #f(x)#

#f(x) =x^3+5x^2+2x-8#

Let #x-1=0 " "rarr x = 1" "# subs 1 for x in the expression

In doing this we are finding the remainder without actually having to divide.

#f(1) = (1)^3+5(1)^2+2(1)-8#

#= 1+5+2-8 = 0#

The fact that the answer is #0#, tells us that the remainder is 0.
Actually, there is no remainder.

(x-1) is a factor of the expression