Question 1

Question 1: State whether the given algebraic expressions are polynomials? Justify. i. y + ii. 2 – 5√x iii. x2 + 7x + 9 iv. 2m-2 + 7m – 5 v. 10

Accepted 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 (neg

Question 2

Question 2: Write the coefficient of m3 in each of the given polynomial. i. m3 ii. + m – √3m3 iii. m3 + 5m2 – 7m -1

Accepted Answer

i. 1 ii. -√3 iii. –

Question 3

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

Accepted Answer

i. 5x7 ii. x35 – 1 iii. 3x8 + 2x6 + x5

Question 4

Question 4: Write the degree of the given polynomials. i. √5 ii. x° iii. x2 iv. √2m10 – 7 v. 2p – √7 vi. 7y – y3 + y5 vii. xyz +xy-z viii. m3n7 – 3m5n + mn

Accepted Answer

i. √5 = √5 x° ∴ Degree of the polynomial = 0

Question 5

Question 5: Classify the following polynomials as linear, quadratic and cubic polynomial. [2 Marks] i. 2x2 + 3x +1 ii. 5p iii. √2 – iv. m3 + 7m2 + m – √7 v. a2 vi. 3r3

Accepted Answer

Linear polynomials: ii, iii Quadratic polynomials: i, v Cubic polynomials: iv, vi

Question 6

Question 6: Write the following polynomials in standard form. i. m3 + 3 + 5m ii. – 7y + y5 + 3y3 – + 2y4 – y2

Accepted Answer

i. m3 + 5m + 3 ii. y5 + 2y4 + 3y3 – y2 – 7y –

Question 7

Question 7: Write the following polynomials in coefficient form. i. x3 – 2 ii. 5y iii. 2m4 – 3m2 + 7 iv. –

Accepted Answer

i. x3 – 2 = x3 + 0x2 + 0x – 2 ∴ Coefficient form of the given polynomial = (1, 0, 0, -2)

Question 8

Question 8: Write the polynomials in index form. i. (1, 2, 3) ii. (5, 0, 0, 0,-1) iii. (-2, 2, -2, 2)

Accepted Answer

i. Number of coefficients = 3 ∴ Degree = 3 – 1 = 2 ∴ Taking x as variable, the index form is x2 + 2x + 3

Question 9

Question 9: Write the appropriate polynomials in the boxes.

Accepted Answer

i. Quadratic polynomial: x2; 2x2 + 5x + 10; 3x2 + 5x ii. Cubic polynomial: x3 + x2 + x + 5; x3 + 9 iii. Linear polynomial: x + 7 iv. Binomial: x + 7; x3 + 9; 3x2 + 5x v. Trinomial: 2x2 + 5x + 10 vi. Monomial: x2

Question 10

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

Accepted Answer

Monomial: x5 Binomial: x5 + x Trinomial: 2x5 – x2 + 5

Question 11

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

Accepted Answer

x3y2 + xy

Chapter 3 Polynomials Practice Set 3.1 Solutions