Question

4. Descompuneţi în factori ireductibili expresiile de mai jos:
b) 2x²-x²-2x + 1;
a) x-x-9x+9;
d) x²-x²-x+ 1;
g) 2x²+x-2x-1;
1x³-4x² - 4x + 16;
e) x²+x²-9x-9;
h) x²³-2x²-x+ 2;
k) x²-2²-4x+8;

Answer 1

b) 2x² - x² - 2x + 1 = x² - 2x + 1 = (x-1)²

a) x³ - x² - 9x + 9 = x²(x-1) - 9(x-1) = (x-1)(x²-9) = (x-1)(x+3)(x-3)

d) x² - x² - x + 1 = -x + 1 = -(x-1)

g) 2x² + x - 2x - 1 = 2x(x-1) - 1(x-1) = (2x-1)(x-1)

f) x³ - 4x² - 4x + 16 = x²(x-4) - 4(x-4) = (x-4)(x²-4) = (x-4)(x+2)(x-2)

e) x² + x² - 9x - 9 = 2x² - 9x - 9 = (2x+3)(x-3)

h) x²³ - 2x² - x + 2 = (x-2)(x²+1)(x²-x+1)(x+1)(x³+x²+1)

k) x² - 2² - 4x + 8 = (x-2)(x+2) - 4(x-2) = (x-2)(x-2) = (x-2)²