Chapter 2: Polynomials

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Q
Polynomials CBSE NCERT Solutions

Question:

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

  1. p(x) = x3- 3x2 + 5x – 3 , g(x) = x2 – 2
  2. p(x) = x4 - 3x2 + 4x + 5 , g(x) = x2 + 1 – x
  3. p(x) = x4 – 5x + 6, g(x) = 2 – x2

Answer:

Solutions:

(i)  p(x) = x3- 3x2 + 5x – 3 , g(x) = x2 – 2

We have,

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

We have,

Dividend = p(x) = x– 3x+ 4x +5

Divisor = g(x) = x2 +1-x

 

Hence, Quotient is  x+ x–3 and Remainder is 8.

 

 

(iii) p(x) = x4 – 5x + 6, g(x) = 2 – x2

We have,

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

Divisor = g(x) = 2 – x2 = –x2 + 2

 

Hence, Quotient is -x2-2 and Remainder is -5x + 10.

 

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