Question

Descompuneti in factori: (Nu se foloseste formula de calcul la descompuneri,help)
a) (x+1) (x+3)^2 -4 (x+1)
b) (x+5) (2x-1)^2- 16(x+5)
c) (x-3)(x+2)^2-x+3
d) (x+7)^2-25

Answer 1

a)

(x+1)(x+3)²-4(x+1)=

x³+6x²+9x+x²+2x×3+3²-4x-4=

x³+6x²+9x+x²+6x+9-4x-4=

x³+(6x²+x²)+(9x+6x-4x)+(9-4)=

x³+7x²+11x+5

b)

(x+5)(2x-1)²-16(x+5)=

4x³-4x²+x+20x²-20x+5-16x-80=

4x³+(-4x²+20x²)+(x-20x-16x)+(5-80)=

4x³+16x²-35x-75

c)

(x-3)(x+2)²-x+3=

x³+4x²+4x-3x²-12x-12-x+3=

x³+(4x²-3x²)+(4x-12x-x)+(-12+3)=

x³+x²-9x-9

d)

(x+7)²-25=

(x+7)²-5²=

(x+7+5)(x+7-5)=

(x+12)(x-2)