Q. 65.0( 1 Vote )
What first degree polynomial added to 2x3 – 3x2 + 5x + 1 gives a multiple of x2 – 1?
Answer :
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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