Divide x³–3x²+x+2 by a polynomial g(x),the quotient and remainder were x–2 and –2x+4.Find g(x)

Class-10,Maths, Ncert, Chapter- Polynomials,

Exercise-2.3
Q1.Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainderin each of the following :

(i)p(x) = x³ – 3x² + 5x – 3,g(x) = x²– 2
(ii)p(x) = x⁴ – 3x² + 4x + 5,g(x)=x² + 1 – x
(iii)p(x) = x⁴ – 5x + 6,g(x) = 2–x²

2.Check whether the first polynomial is a factor of the second polynomial by dividing thesecond polynomial by the first polynomial:
(i)t² – 3, 2t⁴ + 3t³ – 2t² – 9t – 12
(ii)x² + 3x + 1, 3x⁴ + 5x³ – 7x³ + 2x + 2
(iii)x³ – 3x + 1, x⁵ – 4x³ + x² + 3x + 1

Q3.Obtain all other zeroes of 3x⁴ + 6x³ – 2x² – 10x – 5, if two of its zeroes are √5/3 & -√5/3⋅

Q4. Divide x³–3x²+x+2 by a polynomial g(x),the quotient and remainder were x–2 and –2x+4.Find g(x)

What is Division Algorithm for Polynomials with an example?

Exercise-2.2

Q2.
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
(i)1/4,-1(ii)√2,1/3(iii)0,5(iv)1, 1(v)-1/4,1/4(vi)4, 1

Q1.Find the zeroes of the following quadratic polynomials and verify the relationship betweenthe zeroes and the coefficients.
(i)x² – 2x – 8
(ii)4s² – 4s + 1
(iii)6x² – 3 – 7x
(iv)4u² + 8u
(v)t² – 15
(vi)3x² – x – 4

Relationship between Zeroes and Coefficients of a quadratic and a cubic Polynomial.

What is a polynomial ? What is a root or zero of a polynomial ? Classification of Polynomials.

Thanks for Visit.♥️