Question

13. Descompuneți:
a) x3 + x2 - x - 1;
d) x3 + x2 – 25x - 25;
g) 4x - 12x - x + 3;
j) 9x3 + 27x2 - 4x - 12;​

Answer 1

Răspuns:

Explicație pas cu pas:

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

= (x-1)(x+1)(x+1) = (x-1)(x+1)²

d) x³+x²-25x-25 = x²(x+1) - 25(x+1) = (x+1)(x²-25) =

= (x+1)(x-5)(x+5)

g) 4x³-12x²-x+3 = 4x²(x-3)-(x-3) = (x-3)(4x²-1) =

= (x-3)(2x-1)(2x+1)

j) 9x³+27x²-4x-12 = 9x²(x+3)-4(x+3) = (x+3)(9x²-4) =

=(x+3)(3x-2)(3x+2)

g') 4x-12x-x+3 = -9x+3 = (-3)(3x-1)