**Question 1.State whether the given algebraic expressions are polynomials? Justify.**

ii. 2 – 5√x

iii. x^{2} + 7x + 9

iv. 2m^{-2} + 7m – 5

v. 10

Answer:

i. No, because power of v in the term 5√x is -1 (negative number).

ii. No, because the power of x in the term 5√x is

i. e. 0.5 (decimal number).

iii. Yes. All the coefficients are real numbers. Also, the power of each term is a whole number.

iv. No, because the power of m in the term 2m^{-2} is -2 (negative number).

v. Yes, because 10 is a constant polynomial.

**Question 2.Write the coefficient of m ^{3} in each of the given polynomial.i. m^{3}Answer:**

i. 1

ii. -√3

**Question 3.Write the polynomial in x using the given information. [1 Mark each]i. Monomial with degree 7ii. Binomial with degree 35iii. Trinomial with degree 8Answer:**

i. 5x

^{7}

ii. x

^{35}– 1

iii. 3x

^{8}+ 2x

^{6}+ x

^{5}

**Question 4.Write the degree of the given polynomials.i. √5ii. x°iii. x**

^{2}iv. √2m

^{10}– 7v. 2p – √7vi. 7y – y

^{3}+ y

^{5}vii. xyz +xy-zviii. m

^{3}n

^{7}– 3m

^{5}n + mnAnswer:

i. √5 = √5 x°

∴ Degree of the polynomial = 0

ii. x°

∴Degree of the polynomial = 0

iii. x^{2}

∴Degree of the polynomial = 2

iv. √2m^{10} – 7

Here, the highest power of m is 10.

∴Degree of the polynomial = 10

v. 2p – √7

Here, the highest power of p is 1.

∴ Degree of the polynomial = 1

vi. 7y – y^{3} + y^{5}

Here, the highest power of y is 5.

∴Degree of the polynomial = 5

vii. xyz + xy – z

Here, the sum of the powers of x, y and z in the term xyz is 1 + 1 + 1= 3,

which is the highest sum of powers in the given polynomial.

∴Degree of the polynomial = 3

viii. m^{3}n^{7} – 3m^{5}n + mn

Here, the sum of the powers of m and n in the term m^{3}n^{7} is 3 + 7 = 10,

which is the highest sum of powers in the given polynomial.

∴ Degree of the polynomial = 10

**Question 5.Classify the following polynomials as linear, quadratic and cubic polynomial. [2 Marks]i. 2x**

^{2}+ 3x +1ii. 5pv. a

^{2}vi. 3r

^{3}Answer:

Linear polynomials: ii, iii

Quadratic polynomials: i, v

Cubic polynomials: iv, vi

**Question 6.Write the following polynomials in standard form.i. m**

^{3}+ 3 + 5mii. – 7y + y

^{5}+ 3y

^{3}– + 2y

^{4}– y

^{2}Answer:

i. m

^{3}+ 5m + 3

**Question 7.Write the following polynomials in coefficient form.i. x**

^{3}– 2ii. 5yiii. 2m

^{4}– 3m

^{2}+ 7Answer:

i. x

^{3}– 2 = x

^{3}+ 0x

^{2}+ 0x – 2

∴ Coefficient form of the given polynomial = (1, 0, 0, -2)

ii. 5y = 5y + 0

∴Coefficient form of the given polynomial = (5,0)

iii. 2m^{4} – 3m^{2} + 7

= 2m^{4} + Om^{3} – 3m^{2} + 0m + 7

∴ Coefficient form of the given polynomial = (2, 0, -3, 0, 7)

**Question 8.Write the polynomials in index form.i. (1, 2, 3)ii. (5, 0, 0, 0 ,-1)iii. (-2, 2, -2, 2)Answer:**i. Number of coefficients = 3

∴ Degree = 3 – 1 = 2

∴ Taking x as variable, the index form is x

^{2}+ 2x + 3

ii. Number of coefficients = 5

∴ Degree = 5 – 1=4

∴ Taking x as variable, the index form is 5x^{4} + 0x^{3} + 0x^{2} + 0x – 1

iii. Number of coefficients = 4

∴Degree = 4 – 1 = 3

∴Taking x as variable, the index form is -2x^{3} + 2x^{2} – 2x + 2

**Question 9.Write the appropriate polynomials in the boxes.Answer:**

i. Quadratic polynomial: x

^{2}; 2x

^{2}+ 5x + 10; 3x

^{2}+ 5x

ii. Cubic polynomial: x

^{3}+ x

^{2}+ x + 5; x

^{3}+ 9

iii. Linear polynomial: x + 7

iv. Binomial: x + 7; x

^{3}+ 9; 3x

^{2}+ 5x

v. Trinomial: 2x

^{2}+ 5x + 10

vi. Monomial: x

^{2}

**Question 1.Write an example of a monomial, a binomial and a trinomial having variable x and degree 5. ( Textbook pg. no. 3)Answer:**

Monomial: x

^{5}

Binomial: x

^{5}+ x

Trinomial: 2x

^{5}– x

^{2}+ 5

**Question 2.Give example of a binomial in two variables having degree 5. (Textbook pg. no. 38)Answer:**

x

^{3}y

^{2}+ xy