Question

Dane są wielomiany W(x)=x^3-2x+1, Q(x)=-x^3+3x, P(x)=2x+3. Wykonaj wskazane działania.

a) W(x)+Q(x)

b) W(x)-Q(x)

c) W(x)-P(x)

d) W(x)*Q(x)

e) W(x)*P(x)

f) W(x)-P(x)+Q(x)

g) 2W(x)-5Q(x)+W(x)*P(x)

^ potęga

Answer 1

W(x)=x³-2x+1, Q(x)=-x³+3x, P(x)=2x+3

a) W(x)+Q(x)=

=x³-2x+1-x³+3x=

=x+1

 

b) W(x)-Q(x)=

=x³-2x+1-(-x³+3x)=

=x³-2x+1+x³-3x=

=2x³-5x+1

 

c) W(x)-P(x)

=x³-2x+1-(2x+3)=

=x³-2x+1-2x-3=

=x³-4x-2

 

d) W(x)*Q(x)=

=(x³-2x+1)*(x³+3x)=

=x⁶-2x⁴+x³+3x⁴-6x²+3x=

=6x⁶+x⁴+x³-6x²+3x

 

e) W(x)*P(x)

=(x³-2x+1)*(2x+3)=

=2x⁴-4x²+3+3x³-6x+3=

=2x⁴+3x³-4x²-6x+6

 

f) W(x)-P(x)+Q(x)=

=x³-2x+1-(2x+3)-x³+3x=

=x+1-2x-3=

=-x-2

 

g) 2W(x)-5Q(x)+W(x)*P(x)=

=2*(x³-2x+1-)-5*(-x³+3x)+(x³-2x+1)*(2x+3)=

=2x³-4x+2+5x³-15x+2x⁴+3x³-4x²-6x+6=

=2x⁴+10x³-4x²-25x+8