# NCERT Solutions for Class 9 Maths chapter 2 Exercise 2.4 - Polynomials - Free PDF Download

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#### All Questions of Chapter 2 Exercise 2.4

Once you complete the chapter 2 then you can revise Ex. 2.4 by solving following questions

Q1. Determine which of the following polynomials, $(\mathrm{x}+1)$ is a factor of :

(i) $x^{3}+x^{2}+x+1$

(ii) $x^{4}+x^{3}+x^{2}+x+1$

(iii) $x^{4}+3 x^{3}+3 x^{2}+x+1$

(iv) $x^{3}-x^{2}-(2+\sqrt{2}) x+\sqrt{2}$

Q2. Use the factor theorem to determine whether $\mathrm{g}(\mathrm{x})$ is a factor of $\mathrm{p}(\mathrm{x})$ in each of the following cases :

(i) $\mathrm{p}(\mathrm{x})=2 \mathrm{x}^{3}+\mathrm{x}^{2}-2 \mathrm{x}-1, \mathrm{~g}(\mathrm{x})=\mathrm{x}+1$.

(ii) $\mathrm{p}(\mathrm{x})=\mathrm{x}^{3}+3 \mathrm{x}^{2}+3 \mathrm{x}+1, \mathrm{~g}(\mathrm{x})=\mathrm{x}+2$.

(iii) $\mathrm{p}(\mathrm{x})=\mathrm{x}^{3}-4 \mathrm{x}^{2}+\mathrm{x}+6 ; \mathrm{g}(\mathrm{x})=\mathrm{x}-3$

Q3. Find the value of $\mathrm{k}$, if $\mathrm{x}-1$ is a factor of $\mathrm{p}(\mathrm{x})$ in each of the following cases :

(i) $\mathrm{p}(\mathrm{x})=\mathrm{x}^{2}+\mathrm{x}+\mathrm{k}$

(ii) $\mathrm{p}(\mathrm{x})=2 \mathrm{x}^{2}+\mathrm{kx}+\sqrt{2}$

(iii) $\mathrm{p}(\mathrm{x})=\mathrm{kx}^{2}-\sqrt{2} \mathrm{x}+1$

(iv) $p(x)=k x^{2}-3 x+k$

Q4. Factorise :

(i) $12 \mathrm{x}^{2}-7 \mathrm{x}+1$

(ii) $2 \mathrm{x}^{2}+7 \mathrm{x}+3$

(iii) $6 x^{2}+5 x-6$

(iv) $3 \mathrm{x}^{2}-\mathrm{x}-4$

Q5. Factorise :

(i) $x^{3}-2 x^{2}-x+2$

(ii) $x^{3}-3 x^{2}-9 x-5$

(iii) $x^{3}+13 x^{2}+32 x+20$

(iv) $2 \mathrm{y}^{3}+\mathrm{y}^{2}-2 \mathrm{y}-1$

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