Question

$2x^2 - xy + 9y^2$
Find the degree of the polynomial.

Answer 1

Answer:

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

Ans. (i) 4x2 – 3x + 7

⇒ 4x2 – 3x + 7x°

∵ All the exponents of x are whole numbers.

∴ 4x2 – 3x + 7 is a polynomial in one variable.

(ii)

∵ All the exponents of y are whole numbers.

∴ is a polynomial in one variable.

(v) x10 + y3 + t50

∵; Exponent of every variable is a whole number,

∴ x10 + y3 + t50 is a polynomial in x, y and t, i.e. in three variables.

2. Write the co-efficients of x2 in each of the following:

(i) 2 + x2 + x

(ii) 2 – x2 + x3

(iii)

(v)

Ans. (i) 2 + x2 + x

The co-efficient of x2 is 1.

(ii) 2 – x2 + x3

The co-efficient of x2 is (–1).

(iii)

The co-efficient of x2 is

(iv)

∴ The co-efficient of x2 is 0

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

Ans. (i) A binomial of degree 35 can be: 3x35 – 4

(ii) A monomial of degree 100 can be:

4. Write the degree of each of the following polynomials:

(i) 5x3 + 4x2 + 7x (ii) 4 - y2 (iii) (iv) 3

Ans. (i) 5x3 + 4x2 + 7x

∵ The highest exponent of x is 3.

∴ The degree of the polynomial is 3.

(ii) 4 – y2

∵ The highest exponent of y is 2.

∴ The degree of the polynomial is 2.

(iii)

∵ The highest exponent of t is 1.

∴ The degree of the polynomial is 1.

(iv) 3

since, 3 = 3x°

∴ The degree of the polynomial 3 is 0.