Question

6Restringeti:
a) 25X²-10X+1
b)0,25X²+X+1
c)X³-6X²+12X-8
d)X³+3X²+3X+1
7Descompuneti in factori ireductibili polinomul:
a)27x²-10
b)x³+5.
c)2x²-15
8Descompunerea in factori ireductibili polinomul: 
a)(6x+3)²-(5x-4)²
b)8x²-(x-5)³
c)125x³+(x+1)³

Answer 1

a) 25X²-10X+1=(5x-1)(5x-1)=(5x-1)²
c)X³-6X²+12X-8=x²(x-6)+4(3x-2)
d)X³+3X²+3X+1=(x+1)(x²+2x+1)=(x+1)(x+1)(x+1)=(x+1)²
7Descompuneti in factori ireductibili polinomul:
a)27x²-10=0
27x²=10
x²=10/27
x=√10/√27=√10/3√3=√10√3/27=√30/27
c)2x²-15=0
2x²=15
x²=15/2
x=√15/√2=√15√2/2=√30/2
8Descompunerea in factori ireductibili polinomul: 
a)(6x+3)²-(5x-4)²=36x²+36x+9-(25x²-40x+16)=36x²+36x+9-25x²+40x-16=11x²+76x-17
b)8x²-(x-5)³=8x²-(x³-15x²+75x-125)=8x²-x²+15x²-75x+125=-x³+23x²-75x+125
c)125x³+(x+1)³=125x³+x³+3x²+3x+1=126x³+3x²+3x+1