Question

1)Oblicz wartość wielomianów. W(x) 2x³+4x²-x+1 dla x= -3 2) Dane są wielomiany W(x) = -x³+x²-1 i P(x) = -3x²+2 wyznacz W(x) - P(x) i W(x) *P(x) Rozłóż na czynnik wielomian x³-x²-25x+25=0

Answer 1

1) W(-3)= 2*(-3)³+4*(-3)²-(-3)+1=

=2*(-27)+4*9+3+1=

=-54+36+3+1=

=-14

2)

 W(x) = -x³+x²-1

iP(x) = -3x²+2

 W(x) - P(x)=

=-x³+x²-1 - (-3x²+2)=

=-x³+x²-1 +3x²-2=

=-x³+4x²-3

W(x) * P(x)=

=(-x³+x²-1 ) (-3x²+2)=

=3x⁵-2x³-3x⁴+2x²+3x²-2=

=3x⁵-3x⁴-2x³+5x²+-2

3)

x³-x²-25x+25=0

x²(x-1)-25(x-1)=0

(x-1)(x²-25)=0

(x-1)(x-5)(x+5)=0

Answer 2

W(x)=2x³+4x²-x+1

x=-3

W(-3)=2*(-3)³+4*(-3)²-(-3)+1=2*(-27)+4*9+3+1=-54+36+4=-14

 

W(x)=-x³+x²-1

P(x)=-3x²+2

 

W(x)-P(x)=-x³+x²-1-(-3x²+2)=-x³+x²-1-3x²-2=-x³-2x²-3

W(x)*P(x)=(-x³+x²-1)*(-3x²+2)=3x⁵-2x³-3x⁴+2x²+3x²-2=3x⁵-3x⁴+x³+5x²-2

 

x³-x²-25x+25=0

x²(x-1)-25(x-1)=0

(x-1)(x²-25)=0

(x-1)(x+5)(x-5)=0