Question

wyznacz wielomiany f(x) = u(x)*w(x) oraz g(x)= [u(x)]^2 - w(x)

b) u(x)=x⁴-x²+1, w(x)=-6x³+2x²-1

Answer 1

f(x)=u(x)*w(x)

f(x)=(x⁴-x²+1)(-6x³+2x²-1)=-6x⁷+2x⁶-x⁴+6x⁵-2x⁴+x²-6x³+2x²-1=-6x⁷+2x⁶+6x⁵-3x⁴-6x³+3x²-1

g(x)=u²(x)-w(x)=(x⁴-x²+1)²-(-6x³+2x²-1)=(x⁴-x²+1)(x⁴-x²+1)-(-6x³+2x²-1)=x⁸-x⁶+x⁴-x6+x⁴-x²+x⁴-x²+1+6x³-2x²+1=x⁸-2x⁶+3x⁴+6x³-4x²+2