Question

Descompuneti in factori ireductibili:
a) 4(5x-3)^2-9(3x-4)^2
b) 2x^2-x-3
c) x^2-5x-6

Answer 1

Răspuns:

Explicație pas cu pas:

a)

4(5x-3)^2-9(3x-4)^2  =

[2(5x-3)]² - [3(3x-4)]² =

[10x - 6]² - [9x - 12]² =

(10x - 6 + 9x - 12)(10x - 6 - 9x + 12) =

(19x - 18)(x + 6)

b)

2x^2 - x - 3  =

2x² + 2x - 3x - 3 =

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

(x + 1)(2x - 3)

c)

x^2 - 5x - 6 =

= x^2 + x - 6x - 6 =  

= x(x+1) - 6(x+1) =

= (x + 1)(x - 6)

Answer 2

a)4(5x-3)²-9(3x-4)²=

2²×(5x-3)²-3²×(3x-4)²=

(2(5x-3))²-(3(3x-4))²=

(2(5x-3)-3(3x-4))(2(5x-3)+3(3x-4))=

(10x-6-9x+12)(10x-6+9x-12)=

(x+6)(19x-18)

b)2x²-x-3=

2x²+2x-3x-3=

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

(x+1)(2x-3)

c)x²-5x-6=

x²+x-6x-6=

x(x+1)-6(x+1)=

(x+1)(x-6)