Question

Calculati :

1) x³+3x²-x-3

2) $x^{6}$  - $x^{4}$ - 16x²+16

3) x³-2x²-x+2

4) x³-x²-9x+9

5) x³+2x²-x-2

6) x³+3x²-4x-12

7) x³+3x²-9x-27

Answer 1

$1) x^3+3x^2-x-3= x^3-x+3x^2-3 = x(x^2-1)+3(x^2-1)= \\ \\ =(x^2-1)(x+3) = (x-1)(x+1)(x+3) \\ \\ \\2) x^6-x^4-16x^2+16 = x^4(x^2-1)-16(x^2-1) = \\ \\ = (x^2-1)(x^4-16) = (x-1)(x+1)(x^2-4)(x^2+4) = \\ \\ =(x-1)(x+1)(x-2)(x+2)(x^2+4) \\ \\ \\3) x^3-2x^2-x+2= x^3-x-2x^2+2 = x(x^2-1)-2(x^2-1)= \\ \\ =(x^2-1)(x-2) = (x-1)(x+1)(x-2)$


$4) x^3-x^2-9x+9= x^2(x-1)-9(x-1) = (x-1)(x^2-9)= \\ \\ =(x-1)(x-3)(x+3) \\ \\ \\ 5) x^3+2x^2-x-2= x^3-x+2x^2-2 = x^2(x-1)+2(x^2-1) = \\ \\ =(x-1)(x^2+2) \\ \\ \\ 6) x^3+3x^2-4x-12 = x^3-4x+3x^2-12 = x(x^2-4)+3(x^2-4)= \\ \\ =(x+3)(x^2-4)= (x+3)(x-2)(x+2) \\ \\ \\ 7) x^3+3x^2-9x-27 = x^2(x+3)-9(x+3) = \\ \\ =(x+3)(x^2-9) = (x+3)(x-3)(x+3) = (x+3)^2\cdot (x-3)$

Answer 2

$1) x^{3}+3x^{2}-x-3$
$x\cdot(x^{2}-1)+3(x^{2}-1)$
$(x+3)\cdot(x^{2}-1)$
$(x+3)\cdot(x-1)\cdot(x+1)$

$2) x^{6}-x^{4}-16x^{2}+16 \Rightarrow$ Eşti sigur? Mai verifică! Mie nu îmi iese!

$3)x^{3}-2x^{3}-x+2$
$x\cdot(x^{2}-1)-2(x^{2}-1)$
$(x-2)\cdot(x^{2}-1)$
$(x-2)\cdot(x-1)\cdot(x+1)$

$4)x^{3}-x^{2}-9x+9$
$x^{2}\cdot(x-1)-9(x-1)$
$(x^{2}-9)\cdot(x-1)$
$(x-3)\cdot(x+3)\cdot(x-1)$

Mai departe fă tu.... eu nu mai am timp! Hai, că sunt simple!