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

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

(ii) 2 - *x*^{2} + *x*^{3}

(iv) √2*x* - 1

**Answer**

(i) coefficients of *x*^{2} = 1

(ii) coefficients of *x*^{2} = -1

(iii) coefficients of *x*^{2} = π/2

(iv) coefficients of *x*^{2} = 0

Degree of a polynomial is the highest power of the variable in the polynomial.

Binomial has two terms in it. Therefore, binomial of degree 35 can be written as *x*^{35}+ x^{34}.

Monomial has only one term in it. Therefore, monomial of degree 100 can be written as *x*^{100}

Write the degree of each of the following polynomials:

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

(ii) 4 – *y*^{2}

(iii) 5*t* – √7

(iv) 3

**Answer**

(i) 5*x*^{3} has highest power in the given polynomial which power is 3. Therefore, degree of polynomial is 3.

(ii) – *y*^{2} has highest power in the given polynomial which power is 2. Therefore, degree of polynomial is 2.

(iii) 5*t* has highest power in the given polynomial which power is 1. Therefore, degree of polynomial is 1.

(iv) There is no variable in the given polynomial. Therefore, degree of polynomial is 0.

Classify the following as linear, quadratic and cubic polynomial:

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

ANS: Quadratic Polynomial

(ii) *x* - *x*^{3}

ANS: Cubic Polynomial

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

ANS: Quadratic Polynomial

(iv) 1 + *x*

ANS: Linear Polynomial

(v) 3*t*

ANS: Linear Polynomial

(vi) *r*^{2}

ANS: Quadratic Polynomial

(vii) 7*x*^{3}

ANS: Cubic Polynomial