Q6 of 31 Page 245

What first degree polynomial added to 2x3 – 3x2 + 5x + 1 gives a multiple of x2 – 1?

Given, 2x3 – 3x2 + 5x + 1


Need to find the first degree polynomial if added to the equation gets the multiple of x2 – 1


⇒ 2x3 – 3x2 + 5x + 1 can be written as 2(x3 – x2 + x + )


⇒ x3 – x2 + x + = (x2 – 1)(x – a) + b


= x3 – ax2 – x + a + b


∴ a = and a + b =


⇒ b = – 1


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