Question

Efectuati impartirea polinomului P(x)=4X³-3X+5 la binomul Q(x)= X²-1 si scrieti sub forma P(x)= Q(x)·C(x)+R(x)

Answer 1

[tex]\it P(X) : Q(X) = \dfrac{P(X)}{Q(X)} = \dfrac{4X^3-3X+5}{X^2 - 1} = \dfrac{4X^3-4X+X+5}{X^2-1} = \\\;\\ \\\;\\ = \dfrac{4X(X^2-1)+X+5}{X^2-1} = \dfrac{4X(X^2-1)}{X^2-1} +\dfrac{X+5}{X^2-1}= 4X \ rest\ \ X+5[/tex]

[tex]\it C(X) = 4X, \ \ R(X) = X+5 \\\;\\\ 4X^3- 3X+5 = (X^2-1)\cdot 4X+(X+5)[/tex]