Question

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in
each of the following :
(i) p(x) = x³ – 3x² + 5x – 3, g(x) = x² – 2
(ii) p(x) = x⁴ – 3x² + 4x + 5, g(x) = x² + 1 – x
(iii) p(x) = x⁴ – 5x + 6, g(x) = 2 – x²

Answer 1

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Answer 2

(i) $p(x)=x^{3}-3 x^{2}+5 x-3, g(x)=x^{2}-2$

As per given data Dividend = p(x) = $x^{3}-3 x^{2}+5 x-3$

Divisor = g(x)= $x^{2}-2$

Hence, on division we obtain quotient and remainder as Quotient =x-3 Remainder =7x-9.

(ii) $p(x)=x^{4}-3 x^{2}+4 x+5, g(x)=x^{2}+1-x$

As per given data

Dividend =p(x) = $\mathrm{x}^{4}-3 \mathrm{x}^{2}+4 \mathrm{x}+5$

Divisor =g(x) = $x^{2}+1-x$

Hence, on division we obtain quotient and remainder as Quotient = $x^{2}+x-3$  Remainder = 8.

(iii) $p(x)=x^{4}-5 x+6, g(x)=2-x^{2}$

As per given data

Dividend = $\mathrm{p}(\mathrm{x})=\mathrm{x}^{4}-5 \mathrm{x}+6=\mathrm{x}^{4}+0 \mathrm{x}^{2}-5 \mathrm{x}+6$

Divisor = g(x) = $2-x^{2}=-x^{2}+2$

Hence, on division we obtain quotient and remainder as

Quotient = $-x^{2}-2$

Remainder = $-5 x+10$

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