Five mark example problems — task. Mathematics State Board, Class 9.

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Answer variants:

(x - 1) (x - 2)

f (1) \neq f (2)

not exactly divisible

x^{2} - 3 x + 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 \(g(x)\).

Did you find an error?

10. Five mark example problems