(Ex-5c) Q.29 & Q.30

29. 4x⁴ – x² – 12x – 36 
30. a² (b + c) – (b + c)³ 
 

Dear student,
As nothing is mentioned,so I am assuming to factorise the given question.
Q29. 
Sol.  Let p( x ) = 4x⁴ - x² - 12x - 36

= 4x⁴ - ( x² + 12x + 36 )

= 4x⁴ - [ x² + 2 × x × 6 + 6² ]   $\left[\right(x+y{)}^2=x^2+y^2+2xy]$

= ( 2x² )² - ( x + 6 )²     $[x^2-y^2=(x+y\left)\right(x-y\left)\right]$

= [ 2x² + ( x + 6 ) ][ 2x² - ( x + 6 ) ]

= ( 2x² + x + 6 )( 2x² - x - 6 )

= ( 2x² + x + 6 )[ 2x² - 4x + 3x - 6 ]

= ( 2x² + x + 6 ) [ 2x( x - 2 ) + 3( x - 2 )]

= ( 2x² + x + 6 )( x - 2 )( 2x + 3 )

Kindly post the other question in separate thread.
Regards