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

Polynomials

Exercise 2.3

Ncert solutions class 9 chapter 2 exercise 3
Ncert solutions class 9 chapter 2 exercise 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) \(p(x)=kx^2-3x+k\)

4. Factorise:

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

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

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

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

5. Factorise:

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