Question

a)descompuneti in factori polinomul:
4x²+4x+1
z²-z+0,25
9x²+42x+49
9x²-6x+1
b)descompuneti in factori ireductibili polinomul
16y²-25(y+4)²
(2x-9)²-81
64x³+1
z^6 - 125

Answer 1

A)descompuneti in factori polinomul:
4x²+4x+1=(2x+1)²
z²-z+0,25=(z-0,5)²
9x²+42x+49=(3x+7)²
9x²-6x+1=(3x-1)²
b)descompuneti in factori ireductibili polinomul
16y²-25(y+4)²=[4y+25(y+4)][4y-25(y+4)]=(4y+25y+100)(4y-25y-100)=
=(29y+100)(-21y-100)
(2x-9)²-81=(2x-9+9)(2x-9-9)=2x(2x-18)
64x³+1=(4x+1)(16x²-4x+1)
z⁶ - 125=(z²-5)(z⁴+5z²+25)