Question

Zadanie 1

Niech W ( x ) = x3 – 2x2 + 1 i Q ( x) = 2x2 - 1. Oblicz:

a) W( x ) + Q ( x ), b) W( x ) - Q ( x ), c) W( x ) × Q ( x ), d) 2W( x ) + x * Q ( x )

Zadanie 2

Wykonaj działania na wielomianach: H( x )*G( x ) +W( x ):K ( x ),

gdzie: H(x)=2x2 –3x +1, G ( x ) = x2 +x - 2, W ( x) = 4x4 + 2x2 – x, K (x) = x

Answer 1

Zad1

W(x)=x³-2x²+1

Q(x)=2x²-1

a)

(x³-2x²+1)+(2x²-1)=x³

b)

(x³-2x²+1)-(2x²-1)=x³-4x²+2

c)

(x³-2x²+1)(2x²-1)=2x⁵-x³-4x⁴+2x²+2x²-1=2x⁵-4x⁴-x³+4x²-1

d)

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

 

Zad2

(2x²-3x+1)(x²+x-2)+(4x⁴+2x²-x)/x=2x⁴+2x³-4x²-3x³-3x²+6x+x²+x-2+4x³+2x-1=

=2x⁴+3x³-6x²+9x-3