Question

Uporządkuj wielomian:
a) W(x) = (3-2x²)² - 4(x²+1)(x²-4)
b) V(x) = x(1-x)³ - 2x(x+3) + (2-x)²
c) Q(x) = (x-3)³ - 12(x²+3)
d) Z(x) = (2x +1)³ - (x²-2)(x²+1)

Answer 1

A) W(x) = (3-2x²)² - 4(x²+1)(x²-4)=
=9-12x²+4x⁴-4(x⁴-4x²+x²-4)=
=9-12x²+4x⁴-4x⁴+12x²+16=25
b) V(x) = x(1-x)³ - 2x(x+3) + (2-x)²=
=x(1-2x+x²)*(1-x)-2x²-6x+4-4x+x²=
=(1-2x+x²)*(x-x²)-x²-10x+4=
=x-2x²+x³-x²+2x³-x⁴-x²-10x+4=
=-x⁴+3x³-4x²-9x+4
c) Q(x) = (x-3)³ - 12(x²+3)=
=(x-3)*(x²-6x+9)-12x²-36=
=x³-6x²+9x-3x²+18x-27-12x²-36=x³-21x²+27x-63
Z(x) = (2x +1)³ - (x²-2)(x²+1) =
=(2x +1)*(4x²+4x+1)-(x⁴+x²-2x²-2)=
=8x³+8x²+2x+4x²+4x+1-x⁴+x²+2=
=-x⁴+8x³+13x²+6x+3