Question

Dane s ˛a wielomiany: W(x) = −x
3 + 2x − x − 5, P(x) = 2x
2 − x + 1 i Q(x) = 5x + 2.
a) Oblicz: 2W(x) + 3[Q(x) − 2P(x)] =
b) Oblicz: 5Q(x) − [W(x) + 2P(x)] =
c) Oblicz: 2W(x) − [P(x) + 3Q(x)] =
d) Oblicz: 3[W(x) − 2P(x)] + 4Q(x) =

Answer 1

W(x) = -x³+2x²-x-5

P(x) = 2x²-x+1

Q(x) = 5x+2

a) 2W(x) + 3[Q(x) - 2P(x)] =

   = 2(-x³+2x²-x-5) +3[5x+2 - 2(2x²-x+1)] =

   = -2x³+4x²-2x-10 +3(5x+2-4x²+2x-2) =

  =  -2x³+4x²-2x-10 +15x+6-12x²+6x-6 = -2x³-8x²+19x-10

b) 5Q(x) - [W(x) +2P(x)] =

    = 5(5x+2) - [-x³+2x²-x-5 + 2(2x²-x+1)] =

   = 25x+10 -[ -x³+2x²-x-5 +4x²-2x+2 ] =

   = 25x +10 +x³-2x²+x+5 -4x²+2x-2 =

   = x³ -6x²+28x+13

c) 2W(x) - [P(x) + 3Q(x)] =

   = 2(-x³+2x²-x-5) - [2x²-x+1 + 3(5x+2)] =

   = -2x³+4x²-2x-10 -[2x²-x+1 +15x+6] =

   = -2x³+4x²-2x-10 -2x²+x-1-15x-6 =

   = -2x³+2x²-16x-17

d)  3[w(x) - 2P(x)] + 4Q(x) =

   = 3[-x³+2x²-x-5 -2(2x²-x+1)] + 4(5x+2) =

   = 3[-x³+2x²-x-5 -4x²+2x-2] + 20x+8 =

   = -3x³+6x²-3x-15-12x²+6x-6 +20x+8 =

   = -3x³-6x²+23x-10