Question

descompuneti in factori: a) 5x^3-10x^2+6x-12
b) (3x+4y)^2-49y^2
c) x^2-11x+30

Answer 1

a) 5x^3-10x^2+6x-12 =  
   5x^2(x - 2) + 6(x - 2) =
  (x - 2) (5x^2 + 6)

b) (3x+4y)^2-49y^2 = 
    (3x + 4y + 7y) (3x + 4y - 7y) =
    (3x + 11y)(3x - 3y) 

c) x^2 +11x+30  = 
   x^2 + 5x + 6x + 30 = 
   x(x + 5) + 6(x + 5) =
   (x + 5) ( x+ 6) 

   x^2 - 11x + 30 = 
   x^2 - 5x - 6x + 30 = 
   x (x - 5) - 6 (x - 5) = 
   (x - 5) (x - 6) 
   

Answer 2

a) 5x³-10x²+6x-12 =
5x²(x - 2) + 6(x - 2) = (x - 2) (5x² + 6)
b) (3x+4y)²-49y² =
(3x + 4y + 7y)(3x + 4y - 7y) = (3x + 11y)(3x - 3y) 
c) x² -11x+30 = (x - 5)( x - 6)