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Wyznacz sumę u+w oraz różnice u-w wielomianów u i w.
u(x)=- 3x3+ 2x5-x6+7x2+x
w(x)=4x5-x2+x6-3x3


Odpowiedź :

Odpowiedź:

[tex]u(x)=-3x^3+2x^5-x^6+7x^2+x\\\\w(x)=4x^5-x^2+x^6-3x^3\\\\\\u(x)+w(x)\\\\-3x^3+2x^5-x^6+7x^2+x+(4x^5-x^2+x^6-3x^3)=\\\\=-3x^3+2x^5-x^6+7x^2+x+4x^5-x^2+x^6-3x^3=6x^5-6x^3+6x^2+x\\\\\\u(x)-w(x)\\\\-3x^3+2x^5-x^6+7x^2+x-(4x^5-x^2+x^6-3x^3)=\\\\-3x^3+2x^5-x^6+7x^2+x-4x^5+x^2-x^6+3x^3=-2x^6-2x^5+8x^2+x[/tex]