Ncert Solutions Class 9 Chapter 2 Polynomials Exercise 2.3 Question 3

3. Find the value of k, if x – 1 is a factor of p(x) in each of the following cases:

(i) (p(x)=x^2+x+k)

(ii) (p(x)=2x^2+kx+sqrt 2)

(iii) (p(x)=kx^2-sqrt 2 x+1)

(iv) (p(x)=kx^2-3x+k)

Polynomials

Exercise 2.3

Ncert solutions class 9 chapter 2 exercise 3

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Class 9

Polynomials

Exercise 2.3

1. Determine which of the following polynomials has (x + 1) a factor:

(i) (x^3+x^2+x+1)

(ii) (x^4+x^3+x^2+x+1)

(iii) (x^4+3x^3+3x^2+x+1)

(iv) (x^3-x^2-(2+sqrt 2)x+sqrt 2)

2. Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:

(i) (p(x)=2x^3+x^2-2x-1), (g(x)=x+1)

(ii) (p(x)=x^3+3x^2+3x+1), (g(x)=x+2)

(iii) (p(x)=x^3-4x^2+x+6), (g(x)=x-3)

3. Find the value of k, if x – 1 is a factor of p(x) in each of the following cases:

(i) (p(x)=x^2+x+k)

(ii) (p(x)=2x^2+kx+sqrt 2)

(iii) (p(x)=kx^2-sqrt 2 x+1)

(iv) (p(x)=kx^2-3x+k)

(i) (p(x)=12x^2-7x+1)

(ii) (p(x)=2x^2+7x+3)

(iii) (p(x)=6x^2+5x-6)

(iv) (p(x)=3x^2-x-4)

(i) (p(x)=x^3-2x^2-x+2)

(ii) (p(x)=x^3-3x^2-9x-5)

(iii) (p(x)=x^3+13x^2+32x+20)

(iv) (p(y)=2y^3+y^2-2y-1)

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