Question

factorise 2x³-3x²-17x+30

Answer 1

$2 {x}^{3} - 3 {x}^{2} - 17x + 30 = 0 \\ by \: hit \: and \: trail \: x = 2 \: satisfies \: so \: x - 2 \: is \: one \: factor \: of \: polynomial$
now divide polynomial with (x-2)

Answer 2

$\huge \bold{hey!!}$

from given

2x² - 3x² - 17x + 30


=> 2x³ - 4x² + x² - 2x - 15x + 30 <[Spliting term]


=> 2x² ( x - 2 )+ x ( x - 2 ) -15 ( x - 30)


=> (x - 2 ) ( 2x² + x - 15 ) <[Taking common ]


=> (x - 2) ( 2x² + 6x - 5x - 15)


=> ( x - 2 ) { 2x ( x + 3) - 5 ( x + 3)


=> ( x - 2 ) { (2x - 5) ( x + 3 ) }


Hence,


Factor of this polynomial =


$\huge \bold \red {(x - 2)(x + 3(2x - 5)}$


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