Question
Factorise : $4x^4- x^2- 12x - 36$
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Answer
Factorise : $4x^4- x^2- 12x - 36$
$= 4x^4 - ( x^2 + 12x + 36 )$
$= ( 2x^2)^2 - ( x^2 + 2x \times 6x + 6^2 )$
$= ( 2x^2)^2 - ( x + 6 )^2$
$= ( 2x^2 + x + 6 )( 2x^2 - x - 6 )$
$= ( 2x^2 + x + 6 )( 2x^2 - 4x + 3x - 6 )$
$= ( 2x^2 + x + 6 )[ 2x( x - 2 ) + 3( x - 2 )]$
$= ( 2x^2 + x + 6 )[ ( x - 2)( 2x + 3 )]$
$= ( 2x^2 + x + 6 )( x - 2 )( 2x + 3 )$
$= 4x^4 - ( x^2 + 12x + 36 )$
$= ( 2x^2)^2 - ( x^2 + 2x \times 6x + 6^2 )$
$= ( 2x^2)^2 - ( x + 6 )^2$
$= ( 2x^2 + x + 6 )( 2x^2 - x - 6 )$
$= ( 2x^2 + x + 6 )( 2x^2 - 4x + 3x - 6 )$
$= ( 2x^2 + x + 6 )[ 2x( x - 2 ) + 3( x - 2 )]$
$= ( 2x^2 + x + 6 )[ ( x - 2)( 2x + 3 )]$
$= ( 2x^2 + x + 6 )( x - 2 )( 2x + 3 )$
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