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) = x2-3x2 + 4x + 5 , g(x) = x2 + 1-x (iii) p(x) = x2-5x + 6, g(x) = 2-x2

(i)p(x) = x3-3x2+5x–3 , g(x) = x2–2 

As per given data Dividend = p(x) = x3-3x2+5x–3

Divisor = g(x) = x2– 2

 Ncert solutions class 10 chapter 2-2

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

(ii) p(x) = x4-3x2+4x+5 , g(x) = x2+1-x

As per given data

Dividend = p(x) = x4 – 3x2 + 4x +5

Divisor = g(x) = x2 +1-x

Ncert solutions class 10 chapter 2-3

Hence, on division we obtain quotient and remainder as Quotient = x2 + x–3 Remainder = 8

(iii) p(x) =x4–5x+6, g(x) = 2–x2 

As per given data

Dividend = p(x) =x4 – 5x + 6 = x4 +0x2–5x+6

Divisor = g(x) = 2–x2 = –x2+2

Ncert solutions class 10 chapter 2-4

Hence, on division we obtain quotient and remainder as

Quotient = -x2-2

Remainder = -5x + 10 

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