NCERT Solutions For Class 10 Math 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:-

 

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

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