What is the value of #k# for which #(x-1)# is a factor of #(2x^3+9x^2+x+k)#?

1 Answer
Borgeth
Oct 11, 2017

#k = -12#

Explanation:

#f(x) = 2x^3 + 9x^2 + x + k#

If #(x-1)# is a factor, then making #x = 1# would make #(x-1)# equal to 0, and everything else in the equation multiply by that 0, resulting to #f(1) = 0#.

#f(1) = 2*1^3 + 9*1^2 + 1 + k = 0#

#f(1) = 2+9+1+k = 0#

#k = -(2+9+1) = - 12#

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