Algebra bases

Take 10 minutes to prepare this exercise.

Then, if you lack ideas to begin, look at the given clue and start searching for the solution.

A detailed solution is then proposed to you.

If you have more questions, feel to ask then on the forum.

Question

We define polynomials and by:

Do the euclidian division of by

Indice

Determine the real number such that:

is of a degree lower or equal to

Start again with the obtained polynomial to eliminate the term of degree

Solution

We infer that:

The quotient is then and the remainder

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