Question

Se considera polinomul f= x^3 + x^2 - 3X +2
a) Calculati f(0)
b) Determinati catul si restul impartirii polinomului f la X^2-4

Answer 1

f(x)= x³ + x² - 3x + 2


a) f(0)= 0³ + 0² - 3 * 0 +2 = 2
f(0)=2

b)
x³ + x² - 3x + 2 |  x²-4     
-x³       +4x       | x+1
/      x² +x + 2
      -x²     + 4    
             x + 6 <--- restul impartirii

Answer 2

$\displaystyle \mathtt{f=X^3+X^2-3X+2}\\ \\ \mathtt{a)f(0)=?}\\ \\ \mathtt{f(0)=0^3+0^2-3 \cdot 0+2=2}$

$\displaystyle \mathtt{b)} \left\begin{array}{ccc}\mathtt{X^3+X^2-3X+2}\\ \cfrac{\mathtt{-X^3~~~~~+4X~~~~~~~~~}}{}&&\\\mathtt{/~~~X^2+X+2}\\ \mathtt{ \cfrac{-X^2~~~~~~+4}{}}\\ \mathtt{/~~~~~~X+6} \end{array}\right| \left\begin{array}{ccc}\displaystyle \underline{\mathtt{X^2-4~~~~~}}\\ \mathtt{X+1~~~~~} \\ \cfrac{}{}&&\\\\ \cfrac{}{}\\ \end{array}\right \\ \\ \mathtt{R=X+6}\\ \\ \mathtt{C=X+1}$