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

**(i) 4x ^{2} – 3x + 7**

**(ii) y ^{2} + √2**

**(iii) 3√t + t√2**

**(iv) y + ^{ 2}/_{y}**

**(v)x ^{10} +y^{3} + t^{50}**

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) x^{10} +y^{3} + t^{50} is not a polynomial with three variables x , y and t.

**Write the coefficients of x**^{2}in each of the following:

**(i) 2+ x ^{2} + x**

**(ii) 2 – x ^{2} + x^{3}**

**(iii) ^{π}/_{2} . x^{2 }+ x**

**(iv)√2x – 1**

Solution:

(i) 2+ x^{2} + x, coefficient of x^{2} is 1

(ii) 2 – x^{2} + x^{3}, coefficient of x^{2} is -1

(iii) ^{π}/_{2} . x^{2 }+ x, coefficient of x^{2} is ^{π}/_{2}

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

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

Solution:

Binomial of degree 35 can be a^{35} + 10

monomial of degree 100 can be x^{100}

**Write the degree of each of the following polynomials:**

**(i) 5x ^{3} + 4x^{2}+ 7**

**(ii) 4 – y ^{2}**

**(iii) 5t – √7**

**(iv) 3**

Solution:

(i) 5x^{3} + 4x^{2}+ 7, degree of a polynomial is 3 as x^{3} is the highest power.

(ii) 4 – y^{2}, degree of a polynomial is 2 as x^{2} 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 x^{0} is the highest power.

**Classify the following as linear, quadratic and cubic polynomials:**

**(i)x ^{2} + x**

**(ii) x – x ^{3}**

**(iii)y + y ^{2} + 4**

**(iv) 1 + x**

**(v) 3t**

**(vi) r ^{2}**

**(vii) 7x ^{3}**

Solution:

(i)x^{2} + x, is quadratic

(ii) x – x^{3}, _{, }is cubic

(iii)y + y^{2} + 4, is quadratic

(iv) 1 + x, is linear

(v) 3t, is linear

(vi) r^{2}, is quadratic

(vii) 7x^{3}_{, }is cubic

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