a)
x^3 - 5x^2 - 3x + 15=x^2(x-5)-3(x-5)=(x-5)(x^2-3)=(x-5)[x^2-(\sqrt3)^2]=(x-5)(x-\sqrt3)(x+\sqrt3)
b)
(x-3)^2 - x^2=x^2-6x+9-x^2=-6x+9=-3(2x-3)
c)
8x^{10} + x^7 =x^7(8x^3+1)=x^7[(2x)^2+1^3]=x^7(2x+1)(4x^2-2x+1)
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wzór skróconego mnozenia a^3+b^3=(a+b)(a^2-ab+b^2)
d)
-5x^2- 8x -3=-(5x^2+8x+3)=-(5x^2+5x+3x+3)=-[5x(x+1)+3(x+1)]=-(x+1)(5x+3)
f)
\frac{1}{9}x^3+\frac{1}{3}x^2+\frac{1}{4}x=x(\frac{1}{9}x^2+\frac{1}{3}x+\frac{1}{4})=x(\frac{4}{36}x^2+\frac{12}{36}x+\frac{9}{36})=\frac{1}{36}x(4x^2+12x+9)=\frac{1}{36}x(2x+3)^2
g)
49x^4 - 81=7^2x^4-3^4=(7x^2)^2-9^2=(7x^2-9)(7x^2+9)=(\sqrt7-3)(\sqrt7+3)(7x^2+9)