SOLUTION: {{{f(x) = x^3 +6x^2 + kx -4 }}} For what value of k will it have the same remainder when it is divided by both x - 1 and x + 2? My attempt: {{{(1)^3 +6(1)2 + k(1) - 4 = (-2)

Algebra ->  Expressions-with-variables -> SOLUTION: {{{f(x) = x^3 +6x^2 + kx -4 }}} For what value of k will it have the same remainder when it is divided by both x - 1 and x + 2? My attempt: {{{(1)^3 +6(1)2 + k(1) - 4 = (-2)      Log On


   

Question 909077: f%28x%29+=+x%5E3+%2B6x%5E2+%2B+kx+-4+
For what value of k will it have the same remainder when it is divided by both x - 1 and x + 2?
My attempt:
%281%29%5E3+%2B6%281%292+%2B+k%281%29+-+4+=+%28-2%29%5E3+%2B6%28-2%29%5E2+%2B+k%28-2%29+-4
+3+%2B+k+=+12+-+2k+
9+%2B+k+=+-2k
9+=+-1k
+k+=+-9
Apparently that's not the right answer.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the answer is k = 3.

I used synthetic division to sollve for the remaindder.
the details of the arithmetic are shown below.
look below the details for further comments.

$$$

step 1:

for factor of (x-1), use synthetic division by 1.

step 2:

for factor of (x+2), use synthetic division by -2.

setp 3:

set remainder from step 1 equal to remainder from step 2 and solve for k.