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On dividing p $(x)$ by $g (x) = x^{2} - 3$ , a student gets quotient $(x + 1)$ and remainder $(2 x - 5)$ .
Using the division algorithm, what is p $(x)$ ?

Class 10Division AlgorithmAlgebra — Polynomials

A $x^{3} + x^{2} - x - 8$
B $x^{3} + x^{2} - 3 x - 8$
C $x^{3} + x^{2} + x - 8$
D $x^{3} - x^{2} - x - 8$

Step-by-Step Solution

p (x) = (x^{2} - 3) (x + 1) + (2 x - 5) = (x^{3} + x^{2} - 3 x - 3) + (2 x - 5) = x^{3} + x^{2} - x - 8

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Answer: A)

x^{3} + x^{2} - x - 8

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