Question

Descompuneti:
1) x²-4=
2) x²-4x+4=
3)4x²+4x+1=
4)x²-4x+3=
5)4x²-4x=
6)x³+2x²+x=
7) (x-3)³- x+3=
8) x³-x²-x+1=
9)x⁴-1=
10) x⁴+1=
Dau coroana. Clasa 7

Answer 1

1) x²-4 = (x-2) (x+2)
2) x² -4x+4= (x-2)²
3) 4x²+4x+1= (2x+1)²
4)x²-4x+3= x²-4x+4-1 = (x-2)² - 1= (x-2+1) (x-2-1)= (x-1) (x-3)
5)4x² - 4x= 4x(x-1)
6)x³+2x²+x= x(x²+2x+1)= x (x+1)²
7)(x-3)³ -x+3= (x-3)³ - (x-3) = (x-3) [(x-3)²-1]= (x-3) (x-3-1)(x-3+1)= (x-3) (x-4)(x-2)
8) x³-x²-x+1=x² (x-1)-(x-1)= (x-1)(x²-1) = (x-1)(x-1)(x+1)= (x-1)² (x+1)
9) x4 -1 =(x²-1)(x²+1) = (x-1)(x+1)(x²+1)
10)x4+1= x4 + 2x² +1 - 2x²= (x²+1)² -2x² = (x²+1 - x√2) ( x²+1+x√2)