### NCERT Solutions For Class 10 Maths Chapter – 2 Exercise – 2.3

NCERT Solutions For Class 10 Math Chapter – 2 Polynomial Exercise – 2.3

Q1. 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 – x
• P(x) = x4– 3x2 + 4x + 5 g(x) = x2 + 1 – x
• P(x) = x4– 5x + 6 g(x) = 2 – x2

Solution:-

• Here p(x) = x3– 3x2 + 5x – 3 and g(x) = x2 – 2

Dividing p(x) by g(x) =

Quotient = x – 3  Remainder = 7x – 9

• P(x) = x4
3x2 + 4x + 5 and g(x) = x2 + 1 – x

Dividing p(x) by g(x)

Quotient = x2 + x – 3 Remainder = 8

• P(x) = x4– 5x + 6 g(x) = 2 – x2

Quotient = -x2 – 2

Remainder = -5x + 10.

Q2.  Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial.

• T2– 3 , 2t4 + 3t3 – 2t2 – 9t – 12
• X2+ 3x + 1, 3x4 + 5x3 – 7x2 + 2x + 12
• X2+ 3x + 1, x5 – 4x3 + x2 + 3x + 1

Solution:-

• First polynomial = t2– 3

Second polynomial = 2t4 + 3t3 – 2t2 – 9t – 12

Dividing second polynomial by first polynomial.

Remainder is zero.

First polynomial is a factor of second polynomial.

• First polynomial = x2+ 3x + 1

Second polynomial = 3x4 + 5x3 – 7x2 + 2x + 2

Dividing second polynomial by first polynomial  =

Remainder is zero.

First polynomial is a factor of second polynomial.

• First polynomial = x3– 3x + 1

Second polynomial = x5 – 4x3 + x2 + 3x + 1.

Remainder ≠ 0

First polynomial is not a factor of second polynomial.

Q3. Obtain all  zeroes of 3x4 + 6x3 – 2x2 – 10x – 5 , If two of its zeroes are and 5/3 and –5/3

Solution:-

Q4. On dividing x3 – 3x2 + x + 2 by a polynomial g(x) the quotient and remainder were x – 2 and -2x + 4 respectively Find g(x).

Solution:-

Q5. Give examples of polynomial p(x) , q(x) and r(x) which satisfy the division algorithm and:

• deg p(x) = deg q(x)
• Deg q(x) = deg r(x)
• Deg r(x) = 0

Solution:-

• P(x) = 2x2+ 2x + 8

Q(x) = x2 + x + 4

G(x) = 2 and r(x) = 0

• P(x) = x3– x2 + 2x + 3

Q(x) = x + 1

G(x) = x2 – 1 and r(x) = 2x +2

• P(x) = x3– x2 + 2x + 3

G(x) = x2 + 2

Q(x) = x – 1 and r(x) = 5

NCERT Solutions For Class 10 Math Chapter – 2 Polynomial Exercise – 2.3   Q1. Divide the polynomial p(x) by the…