Factorize, by splitting the middle term



Asked by Topperlearning User | 7th Aug, 2017, 01:39: PM

Expert Answer:

                                                            
Here  a = 6, b = 17,  c= 5
 
ac = 6 x 5 = 30
 
6x2  + 17x  +  5
 
= 6x2 + 15x + 2x  + 5
 
= 3x (2x + 5) + 1(2x +5)
 
= (3x + 1)(2x + 5)
 
                                                            
             Here a = 1, b = -14, c = 45
             
  ac = 1 x 45 = 45 = (-9) x (-5)
                
                  x2 - 14x + 45
             
          =  x2 - 9x - 5x + 45 

           =   x( x - 9) - 5( x - 9) 
     
           =  ( x - 9 )( x - 5 )
 
                                                                
            Here a = 3 , b = -1,  c = -4
        
             ac = 3 x (-4) =  -12
 
            b = -1 = (-4) + 3
 
                       3x2  - x  -  4
           
                   =  3x2 - 4x + 3x - 4
 
                  =  x ( 3x - 4) + 1( 3x - 4)
 
                 =  ( 3x - 4 ) (x + 1)
 
                                                          
            Here a = 4 , b = -16,  c = 15
 
                 ac = 4 x 15 = 60
 
                b = -16 = ( -10) + (-6)
 
                    4x2 - 16x + 15
             
                 =  4x2  - 10x - 6x + 15
 
                 =  2x ( 2x - 5) - 3(2x - 5)
 
                =  (2x - 5)( 2x - 3)

Answered by  | 7th Aug, 2017, 03:39: PM