Question

Scrieti expresiile ca diferente de patrate si apoi descompuneti in factori:
a)x²+x-2=
b)x²-x-12=
c)x²-x-6=
d)x²-5x+6=
e)x²+13x+30=
f)x²-15x+56=
g)x²-7x+10=
h)x²+11x+30=
i)x²+13x+22=
j)x²-4x+4-5³

Answer 1

a)x²+x-2=x² - 1  + x -1 =(x -1) (x +1) + ( x -1) = ( x -1) (x+2)
b)x²-x-12= x² - 9  - x -3  = (x -3)(x +3)  - (x + 3) = ( x +3) ( x -4)
c)x²-x-6=x² - 4 - x - 2  = (x -2) (x +2)  - ( x + 2) = (x + 2)(x -3)
d)x²-5x+6=x² - 2x - 3x + 6 = x(x -2)  - 3(x -2) = ( x -2)(x -3)
e)x²+13x+30= x² +10x + 3x + 30 = x(x +10) + 3(x + 10) = ( x +10)(x +3)
f)x²-15x+56= x² - 8x - 7x + 56 =x(x -8)  -7(x -8) = ( x -8)(x -7)
g)x²-7x+10=x² - 2x - 5x + 10 = x( x -2) -5(x -2) = ( x -2)(x -5) 
h)x²+11x+30= x² + 5x + 6x + 30 =x(x +5) + 6(x + 5) = ( x +5)( x +6) 
i)x²+13x+22= x² + 2x + 11x  +22 = x( x +2) + 11( x +2) =( x +2)(x + 11)
j)x²-4x+4 - 5² =( x -2)² - 5² =( x -2 - 5 )( x -2+ 5)