Five mark example problems — task. Mathematics State Board, Class 10.

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1. Find the GCD of the polynomials \(x^3 + x^2 - x + 2\) and \(2x^3 - 5x^2 + 5x - 3\).

Answer:

The GCD of the polynomials is:

\(x^2 - x - 1\)
\(x^2 + x + 1\)
\(x^2 - x + 1\)
\(x^2 + x - 1\)

2. Find the GCD of \(6x^3 - 30x^2 + 60x - 48\) and \(3x^3 - 12x^2 + 21x - 18\).

Answer:

The GCD is:

\(3(x - 2)\)
\(3(x + 2)\)
\(2(x - 3)\)
\(2(x + 3)\)

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