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RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9 PDF Download

RS Aggarwal Solutions: Exercise 2A - Polynomials

Q.1. Which of the following expressions are polynomials? In case of a polynomial, write its degree.
(i) x− 2x+ x + √3
(ii) y+ √3y
(iii)RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9
(iv) x100 − 1
(v)RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9
(vi) x−2 + 2x−1 + 3
(vii) 1
(viii)RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9
(ix)RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9
(x)RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9
(xi)RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9
(xii)RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9
(xiii)RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9

(xiv)RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9
(xv)  2x+ 3x+ √x − 1

Ans.
(i) x5 − 2x3 + x +√3 is an expression having only non-negative integral powers of x. So, it is a polynomial. Also, the highest power of x is 5, so, it is a polynomial of degree 5.
(ii) y+ √3y is an expression having only non-negative integral powers of y. So, it is a polynomial. Also, the highest power of y is 3, so, it is a polynomial of degree 3.
(iii) RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9is an expression having only non-negative integral powers of t. So, it is a polynomial. Also, the highest power of t is 2, so, it is a polynomial of degree 2.
(iv) x100 − 1 is an expression having only non-negative integral power of x. So, it is a polynomial. Also, the highest power of x is 100, so, it is a polynomial of degree 100.
(v) RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9 is an expression having only non-negative integral powers of x. So, it is a polynomial. Also, the highest power of x is 2, so, it is a polynomial of degree 2.
(vix−2+2x−1 + 3 is an expression having negative integral powers of x. So, it is not a polynomial.
(vii) Clearly, 1 is a constant polynomial of degree 0.
(viii) Clearly, RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9 is a constant polynomial of degree 0.
(ix) RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9
This is an expression having negative integral power of x i.e. −2. So, it is not a polynomial.
(x)RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9 is an expression having only non-negative integral power of x. So, it is a polynomial. Also, the highest power of x is 2, so, it is a polynomial of degree 2.
(xi)RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9is an expression having negative integral power of x. So, it is not a polynomial.
(xii) RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9
In this expression, the power of x is 1/2 which is a fraction. Since it is an expression having fractional power of x, so, it is not a polynomial.
(xiii) RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9is an expression having only non-negative integral powers of x. So, it is a polynomial. Also, the highest power of x is 2, so, it is a polynomial of degree 2.
(xiv) RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9
In this expression, one of the powers of x is 3/2 which is a fraction. Since it is an expression having fractional power of x, so, it is not a polynomial.
(xv)RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9
In this expression, one of the powers of x is 1/2 which is a fraction. Since it is an expression having fractional power of x, so, it is not a polynomial.

Q.2. Identify constant, linear, quadratic, cubic and quartic polynomials from the following.
(i) –7 + x
(ii) 6y
(iii) –z3
(iv) 1 – y – y3
(v) x – x3 + x4
(vi) 1 + x + x2
(vii) – 6x2
(viii) – 13
(ix) – p
Ans.
(i) –7 + x is a polynomial with degree 1. So, it is a linear polynomial.
(ii) 6y is a polynomial with degree 1. So, it is a linear polynomial.
(iii) –z3 is a polynomial with degree 3. So, it is a cubic polynomial.
(iv) 1 – y – y3 is a polynomial with degree 3. So, it is a cubic polynomial.
(v) x – x3 + xis a polynomial with degree 4. So, it is a quartic polynomial.
(vi) 1 + x + x2 is a polynomial with degree 2. So, it is a quadratic polynomial.

(vii) – 6x2 is a polynomial with degree 2. So, it is a quadratic polynomial.
(viii) –13 is a polynomial with degree 0. So, it is a constant polynomial.
(ix) – p is a polynomial with degree 1. So, it is a linear polynomial.

Q.3. Write
(i) the coefficient of x3 in x+3x− 5x+ x4.
(ii) the coefficient of x in √3−2√2x + 6x2.
(iii) the coefficient of x2 in 2x – 3 + x3.
(iv) the coefficient of x in RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9
(v) the constant term inRS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9
Ans.
(i) The coefficient of x3 in x+3x2−5x+ x4 is − 5.
(ii) The coefficient of x in √3 − 2√2x + 6x2 is −2√2.

(iii) 2x – 3 + x3 = – 3 + 2x + 0x+ x3

The coefficient of xin 2x – 3 + xis 0.
(iv) The coefficient of x in RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9
(v) The constant term in RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9

Q.4. Determine the degree of each of the following polynomials.
(i) RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9
(ii) y2(y – y3)
(iii) (3x – 2) (2x+ 3x2)

(iv)RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9
(v) – 8
(vi) x–2(x4 + x2)
Ans.
(i) RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9
Here, the highest power of x is 2. So, the degree of the polynomial is 2.
(ii) y2(y – y3) = y3 – y5
Here, the highest power of y is 5. So, the degree of the polynomial is 5.
(iii) (3x – 2)(2x3 + 3x2) = 6x+ 9x3 – 4x3 – 6x2 = 6x4 + 5x3 – 6x2
Here, the highest power of x is 4. So, the degree of the polynomial is 4.
(iv) RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9
Here, the highest power of x is 1. So, the degree of the polynomial is 1.
(v) – 8
–8 is a constant polynomial. So, the degree of the polynomial is 0.
(vi) x–2(x4 + x2) = x2 + x0 = x2 + 1 

Here, the highest power of x is 2. So, the degree of the polynomial is 2

Q.5.
(i) Give an example of a monomial of degree 5.
(ii) Give an example of a binomial of degree 8.

(iii) Give an example of a trinomial of degree 4.
(iv) Give an example of a monomial of degree 0.
Ans.
(i) A polynomial having one term is called a monomial. Since the degree of required monomial is 5, so the highest power of x in the monomial should be 5.
An example of a monomial of degree 5 is 2x5.
(ii) A polynomial having two terms is called a binomial. Since the degree of required binomial is 8, so the highest power of x in the binomial should be 8.
An example of a binomial of degree 8 is 2x8 − 3x.
(iii) A polynomial having three terms is called a trinomial. Since the degree of required trinomial is 4, so the highest power of x in the trinomial should be 4.
An example of a trinomial of degree 4 is 2x4 − 3x + 5.
(iv) A polynomial having one term is called a monomial. Since the degree of required monomial is 0, so the highest power of x in the monomial should be 0.
An example of a monomial of degree 0 is 5.

Q.6. Rewrite each of the following polynomials in standard form.
(i) x−2x+ 8 + 5x3

(ii) 2/3 + 4y− 3y + 2y3
(iii) 6x+ 2x − x− 3x2
(iv) 2 + t − 3t+ t− t2
Ans.
A polynomial written either in ascending or descending powers of a variable is called the standard form of a polynomial.

(i) 8+x−2x2+5x3 is a polynomial in standard form as the powers of x are in ascending order.
(ii) 2/3 − 3y + 4y2+2y3 is a polynomial in standard form as the powers of y are in ascending order.
(iii) 2x−3x+ 6x− x5 is a polynomial in standard form as the powers of x are in ascending order.
(iv) 2 + t − t− 3t3+ t4 is a polynomial in standard form as the powers of t are in ascending order.

The document RS Aggarwal Solutions: Polynomials- 1 | Mathematics (Maths) Class 9 is a part of the Class 9 Course Mathematics (Maths) Class 9.
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FAQs on RS Aggarwal Solutions: Polynomials- 1 - Mathematics (Maths) Class 9

1. What are polynomials?
Ans. Polynomials are algebraic expressions consisting of variables and coefficients, combined using addition, subtraction, multiplication, and exponentiation operations.
2. What is the degree of a polynomial?
Ans. The degree of a polynomial is the highest power of the variable in the expression. It helps determine the complexity of the polynomial and the number of solutions it may have.
3. How can I determine if a given expression is a polynomial?
Ans. To determine if an expression is a polynomial, check if it follows the basic rules of a polynomial: variables should have whole number exponents, only addition, subtraction, multiplication, and exponentiation operations are used, and coefficients should be real numbers.
4. What are the different types of polynomials?
Ans. Polynomials can be classified based on their degree. Some common types include linear polynomials (degree 1), quadratic polynomials (degree 2), cubic polynomials (degree 3), and so on.
5. How are polynomials used in real-life applications?
Ans. Polynomials are used in various fields such as physics, engineering, economics, and computer science to model and solve real-life problems. They help in analyzing data, predicting trends, and making accurate calculations.
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