Question

1)Descompuneti in factori : 25(x+3)²-36. 2) Descompuneti in factori: x²+x-2 8) Descompuneti in factori : a) 9x²-24x+16 ; b)(5x-3)²-(3x-4)²; c) x²-2x-3; d)x²-4x-12

Answer 1

1. 25(x+3)²-36=[5(x+3)]²-6²=(5(x+3)+6)(5(x-3)-6)=(5x+15+6)(5x+15-6)=
(5x+21)(5x+9)
2, x²+x-2=x²-2x+1+3x-3=(x-1)²+3(x-1)=(x-1)(x-1+3)=(x-1)(x+2)
8.a 9x²-24x+16=(3x-4)²
b (5x-3)²-(3x-4)²=(5x-3-3x+4)(5x-3+3x-4)=(2x+1)(8x-7)
c. x²-2x-3=x²+2x+1-4x-4=(x+1)²-4(x+1)=(x+1)(x+1-4)=(x+1)(x-3)
d. x²-4x-12=x²+4x+4-8x-16=(x+2)²-8(x+2)=(x+2)(x+2-8)=(x+2)(x-6)

Answer 2

1. 25(x+3)²-36=5²·(x+3)²- 6²
                       =[5(x+3)- 6][5(x+ 3)+ 6]
                       =(5x+ 15- 6)(15x+15+ 6)
                       =(5x+ 9)(15x+21)

2. x²+x-2        =(x+ 2)(x- 1)

a) 9x²-24x+16=(3x- 4)( 3x- 4)
 
b)(5x-3)²-(3x-4)²= [(5x-3)-(3x-4)][(5x-3)+(3x-4)]
                          =(5x-3-3x+4) (5x-3+3x- 4)
                          =(2x- 1)(8x- 7)

c) x²-2x-3=(x- 3)(x+ 1)
d)x²-4x-12= (x- 6)(x+ 2)