Question

1. Wyznacz wielomiany f(x)=[w(x)]2 i g(x)=[w(x)]2-w(x)

a)w(x)=x2-2x-1

b)w(x)+x3-x2+2

Answer 1

a)

f(x)= (x²-2x-1)(x²-2x-1)= x⁴-2x³-x²-2x³+4x²+2x-x²+2x+1= x⁴-4x³+2x²+4x+1

g(x)=(x²-2x-1)(x²-2x-1)-(x²-2x-1) = x⁴-2x³-x²-2x³+4x²+2x-x+2x+1-x²+2x+1= x⁴-4x³+x²+6x+2

 

b)

f(x)= (x³-x²+2)(x³-x²+2)= x⁶-x⁵+2x³-x⁵+x⁴-2x²+2x³-2x²+4= x⁶-2x⁵+x⁴+4x³-4x²+4

g(x)= (x³-x²+2)(x³-x²+2)-(x³-x²+2)= x⁶-x⁵+2x³-x⁵+x⁴-2x²+2x³-2x²+4-x³+x²-2= x⁶-2x⁵+x⁴+3x³-2x²+2