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 =

Algebra ->  Trigonometry-basics -> 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 =      Log On


   

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) About Me  (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,
%282x%5E2%2B2x%2B9%29%2F%28x%2B3%29=%282x-4%29%2B21%2F%28x%2B3%29
So then multiplying both sides by x%2B3,
2x%5E2%2B2x%2B9=%282x-4%29%28x%2B3%29%2B21
2x%5E2%2B2x%2B9=2x%5E2%2B6x-4x-12%2B21
2x%5E2%2B2x%2B9=2x%5E2%2B2x%2B9
So then verify that,
5x%5E4-4x%5E3%2B3x%5E2-2x%2B1=%285x%5E3%2B6x%5E2%2B15x%2B28%29%28x-2%29%2B57

Answer by stanbon(75887) About Me  (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
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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
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Cheers,
Stan H.
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