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Polynomials CBSE NCERT Solutions
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
- p(x) = x3- 3x2 + 5x – 3 , g(x) = x2 – 2
- p(x) = x4 - 3x2 + 4x + 5 , g(x) = x2 + 1 – x
- p(x) = x4 – 5x + 6, g(x) = 2 – x2
(i) p(x) = x3- 3x2 + 5x – 3 , g(x) = x2 – 2
Dividend = p(x) = x3 - 3x2 + 5x – 3
Divisor = g(x) = x2 – 2
Hence, Quotient is x–3 and Remainder is 7x–9.
(ii) p(x) = x4 - 3x2 + 4x + 5 , g(x) = x2 + 1 - x
Dividend = p(x) = x4 – 3x2 + 4x +5
Divisor = g(x) = x2 +1-x
Hence, Quotient is x2 + x–3 and Remainder is 8.
(iii) p(x) = x4 – 5x + 6, g(x) = 2 – x2
Dividend = p(x) = x4 – 5x + 6 = x4 + 0x2 – 5x + 6
Divisor = g(x) = 2 – x2 = –x2 + 2
Hence, Quotient is -x2-2 and Remainder is -5x + 10.
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