Zadanie Rozłóż wielomian na czynniki a) x do potęgi 3 + 4 x do 2 +4= b)6x do 3 - 5x do 2 +6x - 5 c)x do 3 - 1/2 x do potęgi 2 + x -1/2 d)x do potęgi 3 - 5 x do 2 + 3x-15 e)2x do potęgi 3 - 3 x do 2 - 6 x + 9 f) 10x do 3 +25x do 2 -8x -20 g)x do 5 +10x do 4 +xdo 3 +10 x do 2 h) 3 x do 4 -7x do 3 +3x do 2 - 7x i) x do 6 + 3x do 5+8x do 3 +20x do 2
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a) x do potęgi 3 + 4 x do 2 +4=
x^2(x+4)+4
b)6x do 3 - 5x do 2 +6x - 5 =
=x^2(6x-5)+(6x-5)=
=(6x-5)(x^2+1)
c)x do 3 - 1/2 x do potęgi 2 + x -1/2=
x^2(x-1/2)+(x-1/2)=
=(x-1/2)(x^2+1)
d)x do potęgi 3 - 5 x do 2 + 3x-15=
=x^2(x-5)+3(x-5)=
=(x-5)(x^2+3)
e)2x do potęgi 3 - 3 x do 2 - 6 x + 9=
=x^2(2x-3)-3(2x-3)=
=(2x-3)(x^2-3)
f) 10x do 3 +25x do 2 -8x -20=
=5x^2(2x+5)-4(2x+5)=
=(2x+5)(5x^2-4)
g)x do 5 +10x do 4 +xdo 3 +10 x do 2=
=x^3(x^2+1)+10x^2(x^2+1)=
=(x^2+1)(x^3+10x^2)=x^2(x+10)(x^2+1)
h) 3 x do 4 -7x do 3 +3x do 2 - 7x=
=3x^2(x^2+1)-7x(x^2+1)=
=(x^2+1)(3x-7)x
i) x do 6 + 3x do 5+8x do 3 +20x do 2=
=x^5(x+3)+8x(x+2,5)