Odpowiedź:
a) a= - 9 , b = - 18
b) [tex](x-3)*(x+3)*(x+2)[/tex]
Szczegółowe wyjaśnienie:
a) W(x) = [tex]x^{{3} }+2x^{2} +ax+b[/tex]
W(-1) = -8 , W(2) = -20
[tex]\left \{ {{(-1)^{3} +2*(-1)^{2} +a*(-1) +b = -8} \atop {2^{3} +2*2^{2} +a*2+b = -20}} \right.[/tex]
[tex]\left \{ {{-1+2- a + b = - 8} \atop {8+8+2a +b = - 20}} \right.[/tex]
[tex]\left \{ {{-a+b = -8+1-2} \atop {2a + b = -20-8-8}} \right.[/tex]
[tex]\left \{ {{-a+b = -9} \atop {2a + b=-36}/*(-1)} \right.[/tex]
[tex]\left \{ {{-a+b =-9} \atop {-2a-b = 36}} \right.[/tex]
-----------------
-3a = 27 /:(-3)
a = - 9
-(- 9) + b = -9
b = -9 - 9 = - 18
b) W(x) = [tex]x^{{3} }+2x^{2} - 9 x- 18[/tex] = [tex]x^{2} *(x +2)[/tex][tex]-9*(x+2)[/tex] = [tex](x^{2} -9)*(x+2)[/tex]=[tex](x-3)*(x+3)*(x+2)[/tex]
