Question

Descompuneți în factori , folosind metoda grupării termenilor:
a) x³+3x²-9x-27
b) 2x³-x²-2x+1
c) x³-2x²-4x+8
d) 3x³+x²-12x-4
e) x³-5x²-9x+45
f) 4x³-x²-36x+9

URGENT!! VA ROG!!!!​

Answer 1

$a)x ^ { 3 } + 3 x ^ { 2 } - 9 x - 27$

$x^{2}\left(x+3\right)-9\left(x+3\right)$

$\left(x+3\right)\left(x^{2}-9\right)$

$\left(x-3\right)\left(x+3\right)$

$raspuns = \left(x-3\right)\left(x+3\right)^{2}$

$b)2x ^ { 2 } -x ^ { 2 } -2x+1$

$x^{2}-2x+1$

$a+b=-2$

$ab=1\times 1=1$

$a=-1$

$b=-1$

$\left(x^{2}-x\right)+\left(-x+1\right)$

$x\left(x-1\right)-\left(x-1\right)$

$\left(x-1\right)\left(x-1\right)$

$raspuns = \left(x-1\right)^{2}$

$c)x ^ { 3 } - 2 x ^ { 2 } - 4 x + 8$

$x^{2}\left(x-2\right)-4\left(x-2\right)$

$\left(x-2\right)\left(x^{2}-4\right)$

$\left(x-2\right)\left(x+2\right)$

$raspuns = \left(x+2\right)\left(x-2\right)^{2}$

$d)3 x ^ { 3 } + x ^ { 2 } - 12 x - 4$

$x^{2}\left(3x+1\right)-4\left(3x+1\right)$

$\left(3x+1\right)\left(x^{2}-4\right)$

$\left(x-2\right)\left(x+2\right)$

$raspuns = \left(x-2\right)\left(3x+1\right)\left(x+2\right)$

$e)x ^ { 3 } - 5 x ^ { 2 } - 9 x + 45$

$x^{2}\left(x-5\right)-9\left(x-5\right)$

$\left(x-5\right)\left(x^{2}-9\right)$

$\left(x-3\right)\left(x+3\right)$

$raspuns = \left(x-5\right)\left(x-3\right)\left(x+3\right)$

$f)4 x ^ { 3 } - x ^ { 2 } - 36 x + 9$

$x^{2}\left(4x-1\right)-9\left(4x-1\right)$

$\left(4x-1\right)\left(x^{2}-9\right)$

$\left(x-3\right)\left(x+3\right)$

$raspuns = \left(x-3\right)\left(4x-1\right)\left(x+3\right)$

Sper ca ti-am fost de folos. Succes!!!