Class 9, Maths, Chapter 2, Exercise 2.4, Solutions
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+ $\sqrt{2}$)x + $\sqrt{2}$
Ans:
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 – 4x2 + x + 6, g(x) = x – 3
Ans:
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 + $\sqrt{2}$
(iii) p(x) = kx2 – $\sqrt{2}$ x + 1
(iv) p(x) = kx2 – 3x + k
Ans:
Q.4. Factories:
(i) 12x2 – 7x + 1
(ii) 2x2 + 7x + 3
(iii) 6x2 + 5x – 6
(iv) 3x2 – x–4
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Q.5. Factories:
(i) x3 – 2x2 – x + 2
(ii) x3 – 3x2 – 9x–5
(iii) x3 + 13x2 + 32x + 20
(iv) 2y3 + y2 – 2y – 1
Ans:
