Polynomials (Exercise 2.1)

Polynomials

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Chapter 2

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Exercise 2.1

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EX 2.1 QUESTION 1.

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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) 4x²–3x+7

The given equation has x is the only variable. So, the polynomial in one variable.

(ii) y²+√2

The given equation has y is the only variable. So, the polynomial in one variable.

(iii) 3√t+t√2

= 3 √t^1/2 + √2.t

It is in one variable but not polynomial because it contains (t^1/2) which is not a whole number.

(iv) y+2/y

= y + 2.y^-1

It is in one variable but not polynomial because it contains (y^-1) which is not a whole number.

(v) x¹⁰+y³+t⁵⁰

It is a polynomial in three variables x, y and t. So, it is not a polynomial in one variable.

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EX 2.1 QUESTION 2.

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 Write the coefficients of x² in each of the following:

(i) 2+x²+x

(ii) 2–x²+x³

(iii) (π/2)x²+x

(iii)√2x-1

Solution:

(i) 2 + x² + x.
The coefficient of x² is 1.
(ii)  2 – x² + x³.
The coefficient of x² is -1.
(iii)  + x.
The coefficient of x² is  .
(iv) √2 x – 1.
The coefficient of x² is 0.

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EX 2.1 QUESTION 3.

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

Solution:

(i) A binomial of degree 35 = 3x³⁵ -4.
(ii) A monomial of degree 100 = 3x¹⁰⁰.

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EX 2.1 QUESTION 4.

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Write the degree of each of the following polynomials.
(i) 5x³+4x² + 7x
(ii) 4 – y²
(iii) 5t – √7
(iv) 3

Solution:

(i) The degree of 5x³ + 4x² + 7x = 3.

(ii) The degree of 4- y^{2 =}  2.

(iii) The degree of 5t – √7 = 5t¹ – √7 = 1

(iv) The degree of 3 = 3x° = 0          [∵ x°=1]

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