SOLUTION: Question: Write the function in the form f(x) = (x − k)q(x) + r for the given value of k​and demonstrate that f(k) = r. f(x) = (5x4 −4x3 +3x2 −2x+1); k =

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Question 1031494: Question:
Write the function in the form f(x) = (x − k)q(x) + r for the given value of k​and demonstrate that f(k) = r. f(x) = (5x4 −4x3 +3x2 −2x+1); k = −2
I know that I'm supposed to use synthetic division to solve this
my final answer that I got was 5x^3+6x^2+15x+28 with a remainder of 57/x-2
My question is how do I check my solution to verify?
Thanks!
Found 2 solutions by Fombitz, stanbon:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Work it backwards to see if you get the original numerator.
As a simpler example,

So then multiplying both sides by ,



So then verify that,
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Write the function in the form f(x) = (x − k)q(x) + r for the given value of k​and demonstrate that f(k) = r. f(x) = (5x^4 −4x^3 +3x^2 −2x+1); k = −2
I know that I'm supposed to use synthetic division to solve this
my final answer that I got was 5x^3+6x^2+15x+28 with a remainder of 57/x-2
My question is how do I check my solution to verify?
-------|
-2)....5....-4....3....-2....1
.......5....-14..31....-64..|..129
----------
Checking::
f(-2) = 5*(-2)^4 - 4(-2)^3 + 3(-2)^2 -2(-2) + 1
----
= 5(16) - 4(-8) + 12 + 4 + 1
---
= 80+32+12+4+1 = 129
------------
Cheers,
Stan H.
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