Постройте график функций у=x² + 3x - 18 / x-3

1)
2ху+3х+2у²+3у=(2ху+2у²)+(3х+3у)=2у(х+у)+3(х+у)=(х+у)(2у+3)
2)
ху-у²-х²+у²=(ху+у²)-(х²-у²)=у(х+у)-(х-у)(х+у)=(х+у)(у-х+у)
3)
2х³-16-х²+4=(2х³-16)-(х²-4)=2(х³-2³)-(х-2)(х+2)=2(х-2)(х²+2х+4)-(х-2)(х+2)=
=(х-2)(2х²+4х+8-х-2)=(х-2)(2х²+3х+6)
4)
х³+8-х²-2х=(х³+8)-(х²+2х)=(х³+2³)-х(х+2)=(х+2)(х²-2х+4)-х(х+2)=
(х+2)(х²-2х+4-х)=(х+2)(х²-3х+4)
5)
х²-4х-(х-4)²=(х²-4х)-(х-4)(х-4)=х(х-4)-(х-4)(х-4)=(х-4)(х-х+4)=(х-4)·4=4(х-4)
6)
2х²у²-3у²-2х³+3х=(2х²у²-2х³)-(3у²-3х)=2х²(у²-х)-3(у²-х)=(у²-х)(2х²-3)
7)
у-4ху-1+16х²=(у-4ху)+(16х²-1)=у(1-4х)+(4х-1)(4х+1)=у(1-4х)-(1-4х)(4х+1)=
=(1-4х)(у-4х-1)
8)
2ху-2у-х²+2х-1=(2ху-2у)-(х²-2х+1)=2у(х-1)-(х-1)²=(х-1)(2у-х+1)
9)
у²-х²-у³+х³=(у²-х²)-(у³-х³)=(у-х)(у+х)-(у-х)(у²+ху+х²)=(у-х)(у+х+у²+ху+х²)
УДАЧИ!

1)
2ху+3х+2у²+3у=(2ху+2у²)+(3х+3у)=2у(х+у)+3(х+у)=(х+у)(2у+3)
2)
ху-у²-х²+у²=(ху+у²)-(х²-у²)=у(х+у)-(х-у)(х+у)=(х+у)(у-х+у)
3)
2х³-16-х²+4=(2х³-16)-(х²-4)=2(х³-2³)-(х-2)(х+2)=2(х-2)(х²+2х+4)-(х-2)(х+2)=
=(х-2)(2х²+4х+8-х-2)=(х-2)(2х²+3х+6)
4)
х³+8-х²-2х=(х³+8)-(х²+2х)=(х³+2³)-х(х+2)=(х+2)(х²-2х+4)-х(х+2)=
(х+2)(х²-2х+4-х)=(х+2)(х²-3х+4)
5)
х²-4х-(х-4)²=(х²-4х)-(х-4)(х-4)=х(х-4)-(х-4)(х-4)=(х-4)(х-х+4)=(х-4)·4=4(х-4)
6)
2х²у²-3у²-2х³+3х=(2х²у²-2х³)-(3у²-3х)=2х²(у²-х)-3(у²-х)=(у²-х)(2х²-3)
7)
у-4ху-1+16х²=(у-4ху)+(16х²-1)=у(1-4х)+(4х-1)(4х+1)=у(1-4х)-(1-4х)(4х+1)=
=(1-4х)(у-4х-1)
8)
2ху-2у-х²+2х-1=(2ху-2у)-(х²-2х+1)=2у(х-1)-(х-1)²=(х-1)(2у-х+1)
9)
у²-х²-у³+х³=(у²-х²)-(у³-х³)=(у-х)(у+х)-(у-х)(у²+ху+х²)=(у-х)(у+х+у²+ху+х²)
УДАЧИ!