Question

Descompuneți în factori:​

Answer 1

Răspuns:

Explicație pas cu pas:

20) (2x+1)²-(2x-1)²=(2x+1+2x-1)·(2x+1-2x+1)=4x·2=8·x

21) x³+2x²-x-2=x²(x+2)-(x+2)=(x+2)·(x²-1)=(x+2)·(x+1)·(x-1)

22) x²-6x+5= x²-4x+4-2x+1=(x-2)²-(x-2)= (x-2)·(x-2-1)=(x-2)·(x-3)

23) x²+4x+3= x²+x+3x+3=x·(x+1)+3(x+1)=(x+1)·(x+3)

24) x²-4x+3=x²-x-3x+3=x(x-1)-3(x-1)=(x-1)·(x-3)

25) x²+5x-14=x²-4+5x-10=(x+2)·(x-2)+5·(x-2)=(x-2)·(x+2+5)=(x-2)·(x+7)

26) x²-7x+10=x²-4-7x+14=(x+2)·(x-2)-7(x-2)=(x-2)·(x+2-7)=(x-2)·(x-5)  

27) x²-2x-15=x²-9 -2x-6= (x+3)·(x-3)-2(x+3)=(x+3)·(x-3-2)=(x+3)·(x-5)

28) 12x³-3x=3x·(4x²-1)=3x·(2x+1)·(2x-1)

29) x³-x=x·(x²-1)=x·(x+1)·(x-1)

30) (x²+2x)·(x²+2x+3)+2=(x²+2x)·(x²+2x+1)+(x²+2x)·2+2= (x²+2x)·(x²+2x+1)+2(x²+2x+1)=(x²+2x+1)·(x²+2x+2)