Examine if (5x+2)is factor of 2x³-3x²-17x+30
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2x² - 3x² - 17x + 30
= 2x³ - 4x² + x² - 2x - 15x + 30
= 2x² ( x - 2 )+ x ( x - 2 ) -15 ( x - 30)
= (x - 2 ) ( 2x² + x - 15 )
= (x - 2) ( 2x² + 6x - 5x - 15)
= ( x - 2 ) { 2x ( x + 3) - 5 ( x + 3)
=( x - 2 ) { (2x - 5) ( x + 3 ) }
=(x-2)(2x-5)(x+3)
= 2x³ - 4x² + x² - 2x - 15x + 30
= 2x² ( x - 2 )+ x ( x - 2 ) -15 ( x - 30)
= (x - 2 ) ( 2x² + x - 15 )
= (x - 2) ( 2x² + 6x - 5x - 15)
= ( x - 2 ) { 2x ( x + 3) - 5 ( x + 3)
=( x - 2 ) { (2x - 5) ( x + 3 ) }
=(x-2)(2x-5)(x+3)
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