Polynomial – Exercise 2.1 – Class IX

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

(i) 4x² – 3x + 7

(ii) y² + √2

(iii) 3√t + t√2

(iv) y + ²/_y

(v)x¹⁰ +y³ +  t⁵⁰

Solution:

(i)Polynomial in one variable, x

(ii)Polynomial in one variable, y

(iii) 3√t + t√2 is not  a  polynomial as power of t in √2t is  not a whole number

(iv) y + ²/_y is not a polynomial as a power of  y  in ¹/_y = y^-1  is not a whole number

(v) x¹⁰ +y³ +  t⁵⁰ is not a polynomial with three variables x , y and t.

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

(i) 2+ x² + x

(ii) 2 – x² + x³

(iii) ^π/₂ . x² + x

(iv)√2x – 1

Solution:

(i) 2+ x² + x, coefficient of x² is 1

(ii) 2 – x² + x³, coefficient of x² is -1

(iii) ^π/₂ . x² + x, coefficient of x² is ^π/₂

(iv)√2x – 1, x² is not there therefore there is no coefficient.

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

Solution:

Binomial of degree 35  can be a³⁵ + 10

monomial of degree 100 can be x¹⁰⁰

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

(i) 5x³ + 4x²+ 7

(ii)  4 – y²

(iii)   5t – √7

(iv)  3

Solution:

(i) 5x³ + 4x²+ 7, degree of a polynomial is 3 as x³ is the highest power.

(ii)  4 – y², degree of a polynomial is 2 as x² is the highest power.

(iii)   5t – √7, degree of a polynomial is 1 as x is the highest power.

(iv)  3, degree of a polynomial is 0 as x⁰ is the highest power.

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

(i)x² + x

(ii) x – x³

(iii)y + y² + 4

(iv) 1 + x

(v) 3t

(vi) r²

(vii) 7x³

Solution:

(i)x² + x, is quadratic

(ii) x – x³, _, is cubic

(iii)y + y² + 4, is quadratic

(iv) 1 + x, is linear

(v) 3t, is linear

(vi) r², is quadratic

(vii) 7x³_, is cubic

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