1.10.13 Polynomials
Condition: Find the remainder of the division of the polynomial \( 3 x^{5}+5 x^{4}+3 x^{3}+4 x \) by the polynomial \( 6 x^{3}+5 x^{2}+4 x+5 \) in the ring \( \mathbb{Z} / 7 \mathbb{Z}[x]\).
Polynomials and their complex, real and rational roots. Decomposition in various numerical fields.