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)

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)

Question 909077:
For what value of k will it have the same remainder when it is divided by both x - 1 and x + 2?
My attempt:

Apparently that's not the right answer.

Answer by Theo(13342) (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.

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