# RD Sharma Class 9 Factorisation of Polynomials Exercise 6.1 Solutions

On this page you will find Maths RD Sharma Class 9 Factorisation of Polynomials Exercise 6.1 Solutions. The solutions provided here are to help students practice math problems and get better at solving difficult chapter questions. Maths chapter 6 for class 9 deals with the topic of triangles and it is one of the most important chapters.

## Download RD Sharma Class 9 Factorisation of Polynomials Exercise 6.1 Solutions in PDF

Students can use these solutions to overcome the fear of maths and the solutions have been designed in such a way that it enables them to discover easy ways to solve different problems. These solutions can help students in refining their maths fluency and problem-solving skills. Students can go through the RD Sharma solutions for class 9 chapter 6 Factorisation of Polynomials Exercise 6.1 below and it will be beneficial for them.

## RD Sharma Class 9 Factorisation of Polynomials Exercise 6.1 Solutions

Q1. Which of the following expressions are polynomials in one variable and which are not?
1. $3 x^{2}-4 x+15$
2. $\mathrm{y}^{2}+2 \sqrt{3}$
3. $3 \sqrt{\mathrm{x}}+\sqrt{2} \mathrm{x}$
4. $\mathrm{X}-\frac{4}{\mathrm{x}}$
5. $x^{12}+y^{2}+t^{50}$
Sol:
1. $3 x^{2}-4 x+15-$ it is a polynomial of $x$
2. $\mathrm{y}^{2}+2 \sqrt{3}$ – it is a polynomial of $\mathrm{y}$
3. $3 \sqrt{\mathrm{x}}+\sqrt{2} \mathrm{x}-$ it is not a polynomial since the exponent of $3 \sqrt{\mathrm{x}}$ is not a positive term
4. $\mathrm{x}-\frac{4}{\mathrm{x}}-\mathrm{it}$ is not a polynomial since the exponent of $-\frac{4}{\mathrm{x}}$ is not a positive term
5. $\mathrm{x}^{12}+\mathrm{y}^{2}+\mathrm{t}^{50}-\mathrm{it}$ is a three variable polynomial which variables of $\mathrm{x}, \mathrm{y}, \mathrm{t}$

Q2. Write the coefficients of $\mathrm{x}^{2}$ in each of the following
1. $17-2 x+7 x^{2}$
2. $9-12 \mathrm{x}+\mathrm{x}^{2}$
3. $\frac{\Pi}{6} x^{2}-3 x+4$
4. $\sqrt{3} \mathrm{x}-7$
Sol:
Given, to find the coefficients of $\mathrm{x}^{2}$
1. $17-2 \mathrm{x}+7 \mathrm{x}^{2}-$ the coefficient is 7
2. $9-12 \mathrm{x}+\mathrm{x}^{2}-$ the coefficient is 0
3. $\frac{\prod}{6} x^{2}-3 x+4-$ the coefficient is $\frac{\prod}{6}$
4. $\sqrt{3} \mathrm{x}-7$ – the coefficient is 0

Q3. Write the degrees of each of the following polynomials:
1. $7 x^{3}+4 x^{2}-3 x+12$
2. $12-x+2 x^{2}$
3. $5 y-\sqrt{2}$
4. $7-7 x^{0}$
5. 0
Sol:
Given, to find degrees of the polynomials
Degree is highest power in the polynomial
1. $7 x^{3}+4 x^{2}-3 x+12-$ the degree is 3
2. $12-x+2 x^{3}-$ the degree is 3
3. $5 \mathrm{y}-\sqrt{2}-$ the degree is 1
4. $7-7 \mathrm{x}^{0}-$ the degree is 0
5. $0-$ the degree of 0 is not defined

Q4. Classify the following polynomials as linear, quadratic, cuboc and biquadratic polynomials:
1. $x+x^{2}+4$
2. $3 x-2$
3. $2 \mathrm{x}+\mathrm{x}^{2}$
4. $3 \mathrm{y}$
5. $\mathrm{t}^{2}+1$
f. $7 t^{4}+4 t^{2}+3 t-2$
Sol:
Given
1. $\mathrm{x}+\mathrm{x}^{2}+4$ – it is a quadratic polynomial as its degree is 2
2. $3 x-2-$ it is a linear polynomial as its degree is 1
3. $2 \mathrm{x}+\mathrm{x}^{2}-$ it is a quadratic polynomial as its degree is 2
4. $3 \mathrm{y}$ – it is a linear polynomial as its degree is 1
5. $\mathrm{t}^{2}+1-$ it is a quadratic polynomial as its degree is 2
if $.7 \mathrm{t}^{4}+4 \mathrm{t}^{2}+3 \mathrm{t}-2-\mathrm{it}$ is a bi- quadratic polynomial as its degree is 4

Q5. Classify the following polynomials as polynomials in one variables, two – variables etc:
1. $x^{2}-x y+7 y^{2}$
2. $x^{2}-2 t x+7 t^{2}-x+t$
3. $t^{3}-3 t^{2}+4 t-5$
4. $x y+y z+z x$
Sol:
Given
1. $x^{2}-x y+7 y^{2}-$ it is a polynomial in two variables $x$ and $y$
2. $x^{2}-2 t x+7 t^{2}-x+t-i t$ is a polynomial in two variables $x$ and $t$
3. $\mathrm{t}^{3}-3 \mathrm{t}^{2}+4 \mathrm{t}-5-$ it is a polynomial in one variable $\mathrm{t}$
4. $x y+y z+z x-i t$ is a polynomial in 3 variables in $x, y$ and $z$

Q6. Identify the polynomials in the following:
1. $f(x)=4 x^{3}-x^{2}-3 x+7$
2. $b \cdot g(x)=2 x^{3}-3 x^{2}+\sqrt{x}-1$
3. $\mathrm{p}(\mathrm{x})=\frac{2}{3} \mathrm{x}^{2}+\frac{7}{4} \mathrm{x}+9$
4. $\mathrm{q}(\mathrm{x})=2 \mathrm{x}^{2}-3 \mathrm{x}+\frac{4}{\mathrm{x}}+2$
5. $h(x)=x^{4}-x^{\frac{3}{2}}+x-1$
6. $\mathrm{f}(\mathrm{x})=2+\frac{3}{\mathrm{x}}+4 \mathrm{x}$
Sol:
Given
1. $\left(f(x)=[\right.$ latex $\left.] 4 x^3-x^2-3 x+7 \right) \left(4 x^3-x^2-3 x+7\right]^{\prime \prime}>-$ it is a polynomial
2. b. $\left.[\operatorname{latex}] g(x)=2 x^3-3 x^2+{sgrt}\{x\}-1 \right)-$ it is not a polynomial since the exponent of $\sqrt{x}$ is a negative integer
3. $\backslash\left(\mathrm{p}(\mathrm{x})=[\mathrm{latex}]\left(\operatorname{frac}\{2\}\{3\} x^2\}\right.\right.$ $+\lfloor\operatorname{frac}\{7\}\{4\} x+9 ) \left(\operatorname{frac}\{2\}\{3\} x^2+\operatorname{frac}\{7\}\{4\} x+9 \right]^{n}>$ – it is a polynomial as it has positive integers as exponents
4. [latex $\left.] q(x)=2 x^2-3 x+\operatorname{frac}\{4\}\{x\}+2\right)-$ it is not a polynomial since the exponent of $\frac{4}{x}$ is a negative integer
5. $h(x)=x^{4}-x^{\frac{3}{2}}+x-1-$ it is not a polynomial since the exponent of $-x^{\frac{3}{2}}$ is a negative integer
6. $\mathrm{f}(\mathrm{x})=2+\frac{3}{\mathrm{x}}+4 \mathrm{x}-$ it is not a polynomial since the exponent of $\frac{3}{\mathrm{x}}$ is a negative integer

Q7. Identify constant, linear, quadratic abd cubic polynomial from the following polynomials:
1. $\mathrm{f}(\mathrm{x})=0$
2. $g(x)=2 x^{3}-7 x+4$
3. $\mathrm{h}(\mathrm{x})=-3 \mathrm{x}+\frac{1}{2}$
4. $\mathrm{p}(\mathrm{x})=2 \mathrm{x}^{2}-\mathrm{x}+4$
5. $\mathrm{q}(\mathrm{x})=4 \mathrm{x}+3$
6. $\mathrm{r}(\mathrm{x})=3 \mathrm{x}^{3}+4 \mathrm{x}^{2}+5 \mathrm{x}-7$
Sol:
Given,
1. $\mathrm{f}(\mathrm{x})=0-\mathrm{as} 0$ is constant, it is a constant variable
2. $\mathrm{g}(\mathrm{x})=2 \mathrm{x}^{3}-7 \mathrm{x}+4$ – since the degree is 3 , it is a cubic polynomial
3. $\mathrm{h}(\mathrm{x})=-3 \mathrm{x}+\frac{1}{2}$ – since the degree is 1 , it is a linear polynomial
4. $\mathrm{p}(\mathrm{x})=2 \mathrm{x}^{2}-\mathrm{x}+4$ – since the degree is 2 , it is a quadratic polynomial
5. $\mathrm{q}(\mathrm{x})=4 \mathrm{x}+3$ – since the degree is 1 , it is a linear polynomial
6. $\mathrm{r}(\mathrm{x})=3 \mathrm{x}^{3}+4 \mathrm{x}^{2}+5 \mathrm{x}-7$ – since the degree is 3 , it is a cubic polynomial

Q8. Give one example each of a binomial of degree 25 , and of a monomial of degree 100
Sol:
Given , to write the examples for binomial and monomial with the given degrees
Example of a binomial with degree $25-7 \mathrm{x}^{35}-5$
Example of a monomial with degree $100-2 \mathrm{t}^{100}$

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