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NCERT SOLUTIONS CLASS 9 MATHEMATICS

Exercise 2.4

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

(i) x3 + x2 + x + 1 (ii) x4 + x3 + x2 + x + 1

(iii) x4 + 3x3 + 3x2 + x + 1 (iv) x3 - x2 - (2 + 2)x + 2

Q.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) = 2x3 + x2 - 2x - 1, g(x) = x + 1

(ii) p(x) = x3 + 3x2 + 3x + 1, g(x) = x + 2

(iii) p(x) = x3 - 4 x2 + x + 6, g(x) = x - 3

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

(i) p(x) = x2 + x + k (ii) p(x) = 2x2 + kx +  2

(iii) p(x) = kx2 - √2x + 1

(iv) p(x) = kx2 - 3x + k

Q.4. Factorise:

(i) 12x2 + 7x + 1 (ii) 2x2 + 7x + 3

(iii) 6x2 + 5x - 6 (iv) 3x2 - x - 4

Q.5. Factorise:

(i) x3 - 2x2 - x + 2 (ii) x3 - 3x2 - 9x - 5

(iii) x3 + 13x2 + 32x + 20 (iv) 2y3 + y2 - 2y - 1