Answer :

Given, 2x^{3} – 3x^{2} + 5x + 1

Need to find the first degree polynomial if added to the equation gets the multiple of x^{2} – 1

⇒ 2x^{3} – 3x^{2} + 5x + 1 can be written as 2(x^{3} – x^{2} + x + )

⇒ x^{3} – x^{2} + x + = (x^{2} – 1)(x – a) + b

= x^{3} – ax^{2} – x + a + b

∴ a = and a + b =

⇒ b = – 1

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