Question

Descompuneti in factori:(x²+3x+2)²-(x+1)²

Descompuneti in factori ireductibili:

(x²+2x-3)²-(x-1)²​

Answer 1

(x^2 + 3x + 2)^2 - (x + 1)^2 = [(x + 1)(x + 2)]^2 - ((x + 1)^2 = (x + 1)^2 × [(x + 2)^2 - 1] = (x + 1)^2 × (x + 2 - 1) × (x + 2 + 1) = (x + 1)^2 × (x + 1) × (x + 3) = (x + 1)^3 × (x + 3)

(x^2 + 2x - 3)^2 - (x - 1)^2 = (x^2 + 2x - 3 + x - 1) × (x^2 + 2x - 3 - x + 1) = (x^2 + 3x - 4) × (x^2 + x - 2) = (x - 1)(x + 4) × (x - 1)(x + 2) = (x - 1)^2 × (x + 2) × (x + 4)

Answer 2

Răspuns:

Explicație pas cu pas:

Diferente de patrate, unde folosim formula

a^2 - b^2 = (a-b)(a+b).

* (x²+3x+2)²-(x+1)² =

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

(x^2 + 2x + 1)(x^2 + 4x + 3) =

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

(x+1)^3 (x+3).

*  (x²+2x-3)²-(x-1)²​ =

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

(x^2 + x - 2)(x^2 + 3x - 4) =

(x-1)(x+2)(x+4)(x-1). Asa ramane!!!

Nu scrii (x-1)^2 mai sus pt ca in acest caz acest factor nu ar mai fi IREDUCTIBIL.