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Answer variants:
(x1)(x2)
f(1)f(2)
not exactly divisible
x23x+2
(x+1)(x+2)
exactly divisible
\(0\)
f(1)=f(2)=0
Without actual division, prove that \(f(x) = 2x^4 - 6x^3 + 3x^2 + 3x - 2\) is exactly divisible by \(x^2 - 3x + 2\).
 
Answer:
 
\(f(x) = 2x^4 - 6x^3 + 3x^2 + 3x - 2\)
 
\(g(x) =\)
 
Simplifying \(g(x)\), we get:
 
\(g(x) =\)
 
\(f(1) =\)
 
\(f(2) =\)
 
Since
, then \(f(x)\) is 
by \(g(x)\).