# Polynomials – Exercise 2.1 – (MATHEMATICS) – 9th Class

**Exercise 2.1**

1. Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

(i) 4x² = 3x + 7

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Ans.- is a polynomial in variable x, as exponents of the variable in different terms are whole numbers.

(ii) y² +

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Ans.- is a polynomial in variable y, as exponent of variable y is a whole number.

(iii)

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Ans.- t is not a polynomial, as exponent of variable t in first term, i.e., 3 t 1/2 is not a whole number.

(iv)

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Ans.- is not a polynomial, as exponent of the variable y in the term 2y-1 is not a whole number.

(v)

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Ans.- x10 + y3 + t50 is a polynomial in three variables.

2. Write the coefficient of x2 in each of the following :

(i) 2 + x2 + x

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Ans. – Coefficient of x² in 2 + x² + x is 1 .

(ii) 2 – x2 + x3

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Ans. – Coefficient of x² in 2 – x² + x³ is – 1.

(iii)

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Ans. – Coefficient of x² in is

(iv)

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Ans. – Coefficient of x² in – 1 is 0.

3. Give one example each of a binomial of degree 35, and of a monomial of degree 100.

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Sol.

(i) Binomial of degree 35 is 2×35 + x.

(ii) Monomial of degree 100 is – 7×100

4. Write the degree of each of the following polynomials:

(i) 5×3 + 4×2 + 7x

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Ans. – Degree of polynomial is 3.

(ii) 4 – y2

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Ans. – Degree of polynomial 4 – y2 is 2.

(iii) 5t –

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Ans. – Degree of polynomial 5t – is 1.

(iv)

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Ans. – Degree of polynomial 3 is o.

5. Classify the following as linear, quadratic and cubic polynomials :

(i) x2 + x

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Ans. – Polynomial x2 +x ia a quadratic polynomial.

(ii) x-x3

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Ans. – Polynomial x – x³ is a cubic polynomial.

(iii) y + y2+4

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Ans. – Polynomial y + y² + 4 is a quadratic polynomial.

(iv) 1 + x

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Ans. – Polynomial 1 + x is a linear polynomial.

(v) 3t

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Ans. – Polynomial 3t is a linear polynomial.

(vi) r2

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Ans. – Polynomial r2 is a quadratic polynomial.

(vii) 7×3

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Ans. – Polynomial 7×3 is a cubic polynomial.

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