2 szkoły ponadpodstawowej

II liceum

II technikum

Matematyka 2.  Zakres podstawowy. Po gimnazjum

a) W(x)=3x3−15x2=      =3x2⋅x−3x2⋅5=      =3x2(x−5)

Rozwiązanie 1

a) W(x)=2x3+2x2−8x−8=    =2x2(x+1)−8(x+1)=    =(x+1)⋅(2x2−8)=    =(x+1)⋅2⋅(x2−4)=    =(x+1)⋅2⋅(x−2)⋅(x+2)=

a)   Skorzystamy ze wzoru skróconego mnożenia na różnicę kwadratów:  a2−b2=(a−b)⋅(a+b)      W(x)=9x4−81=9⋅(x4−9)            =9⋅((x2)2−32)=            =9⋅(x2−3)⋅(x2+3)=            =9⋅(x−3<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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a) W(x)=x3−2x+1=      =x3−x−x+1=      =x(x2−1)−x+1=      =x(x−1)​​⋅(x+1)−1⋅(x−1)​​=       =(x−1)⋅[x(x+1)−1]=