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Show that (x-2) is a factor of the polyn...

Show that `(x-2)` is a factor of the polynomial `f(x)=2x^3-3x^2-17 x+30` and hence factorize `f(x)dot`

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`f(x)=2x^3-3x^2-17 x+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 ) }`
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