Question

factories : 2x³ - 3x² - 17x + 30​

Answer 1

Answer:

{(x - 2). (2x - 5). ( x+3)

Step-by-step explanation:

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 =

{(x - 2). (2x - 5). ( x+3)

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Answer 2

$\star\:\:\:\bf\underline\blue{Question:-}$

•     Factorise the given cubic polynomial.

$\star\:\:\:\bf\underline\blue{Solution:-}$

$2x^{3}-3x^{2}-17x+30$

$=2x^{3}-4x^{2}+x^{2}-2x-15x+30$

$=2x^{2}(x-2)+x(x-2)-15(x-2)$

$=(x-2)(2x^{2}+x-15)$

$=(x-2)(2x^{2}+6x-5x-15)$

$=(x-2)(2x(x+3)-5(x+3))$

$=(x-2)(2x-5)(x+3)$

$\star\:\:\:\bf\underline\blue{Answer:-}$

•     Factorised form of the given cubic polynomial is $=(x-2)(2x-5)(x+3)$.