Question

Descompuneți în factori ireductibili: a) (3x-2)²-16x² b) 9(x-2)²-4x² c) 9x³+9x²-4x-4 c)9x³+9x²-4x-4 d) 4(x+5)²-(x-1)²​

Answer 1

Răspuns:

Explicație pas cu pas:

a) (3x-2)²-16x² = (3x - 2 - 4x)(3x - 2 + 4x) = (-2 - x)(-2 + 7x)

b) 9(x-2)²-4x² = [3(x - 2) - 2x)][(3(x - 2) + 2x] = (3x - 6 - 2x)(3x - 6 + 2x) =

(x - 6)(5x - 6)

c) 9x³+9x²-4x-4 = 9x^2 (x + 1) - 4(x + 1) = (x + 1)(9x^2 - 4) =

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

d) 4(x+5)²-(x-1)²​ = [2(x + 5) - (x - 1)][2(x + 5) + (x - 1)]

= (2x + 10 - x + 1)(2x + 10 + x - 1) = (x + 11)(3x + 9) = 3(x + 11)(x + 3)