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## Answers

__Using remainder theorem ,factorise: 2 x__

__³__

__- 13 x__

__²__

__+ 26 x -15__**⇒ Before Factorizing it , let find the value of x in p ( x ), Therefore we get as follows ;-**

**⇒ p ( x ) = 2 x³ – 13 x² + 26 x – 15**

**⇒**

**Now, take x as 1 , we get as ,**

**⇒ p ( 1 ) = 0**

**⇒**

**Hence we can say that , -**

**( x – 1 ) is factor of p ( x )**

**When we divide p( x ) by ( x – 1 ), we get the answer as (2x**

**²**

**– 11x + 15**)

⇒ 2 x³ – 13 x² + 26 x – 15 = ( x – 1 )( 2 x² – 11 x + 15)

⇒ ( x – 1 ) ( 2 x² – 6 x – 5 x + 15 )

⇒ ( x – 1 ) [ 2 x ( x – 3 ) – 5 ( x – 3 )]

__⇒__

__( x – 1 ) ( x – 3 ) ( 2 x – 5 ) is the answer.__