Five mark exercise problems - I — task. Mathematics State Board, Class 10.

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1. Find the least common multiple of \(xy(k^2 + 1) + k(x^2 + y^2)\) and \(xy(k^2 - 1) + k(x^2 - y^2)\)

Answer:

The LCM is:

\((ky - x)(k^2x^2 + y^2)\)
\((ky - x)(k^2x^2 - y^2)\)
\((ky + x)(k^2x^2 + y^2)\)
\((ky + x)(k^2x^2 - y^2)\)

2. Find the GCD of the following by division algorithm \(2x^4 + 13x^3 + 27x^2 + 23x + 7\), \(x^3 + 3x^2 + 3x + 1\), \(x^2 + 2x + 1\)

Answer:

The GCD is:

\(x^2 + 2x + 1\)
\(2x^4 + 13x^3 + 27x^2 + 23x + 7\)
\(x^3 + 3x^2 + 3x + 1\)

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