Degree of a Polynomial

Q.

Write the degree of each polynomial given below:

(i) $xy+7z$ (ii) $x^2-6x^3+8$

(iii) $y-6y^2+5y^8$ (iv) $xyz-3$

(v) $xy+y{z}^2-z{x}^3$ (vi) $x^5{y}^7-8x^3{y}^8+10x^4{y}^4{z}^4$

Q.

Divide the given polynomial by the given monomial.

$\left(i\right)(5x^2-6x)÷3x$

$\left(ii\right)(3y^8-4y^6+5y^4)÷y^4$

$\left(iii\right)8(x^3{y}^2{z}^2+x^2{y}^3{z}^2+x^2{y}^2{z}^3)÷4x^2{y}^2{z}^2$

$\left(iv\right)(x^3+2x^2+3x)÷2x$. [4 MARKS]

Q.

Which of the following expressions are polynomials?
(i) $x^2+4$
(ii) $4-x^{-1}$
(iii) $2x^2-\frac{2}{x}$

1. i

2. i, ii, iii

3. iii

4. ii, iii

Q. Find the simplified value of ab + 2ab.

1. ab
2. 2ab
3. -ab
4. 3ab

Q.

Degree of the algebraic expression '$2$' is

1. 0

2. 1

3. none of the above

4. 2

Q. Which among the following fails to become a degree of an algebraic polynomial?

1. 0
2. 4
3. 10
4. -5

Q. Which of the following cannot be a polynomial's degree?

1. Natural number
2. $0$
3. Negative number
4. Fractional number

Q. When you multiply a polynomial of degree 2 by a polynomial of degree 4, what is the degree of the product?

1. 6
2. 4
3. 8
4. 2

Q.

What is the unit digit of the number $5^{25}$ × $6^{36}$?

1. 0

2. 5

3. 6

4. 1

Q.

Identify the polynomials and mention their degrees.

$x^2+3x+2$

Q.

Write the degree of each polynomial given below:

(i) $xy+7z$
(ii) $x^2-6x^3+8$
(iii) $y-6y^2+5y^8$
(iv) $xyz-3$
(v) $xy+y{z}^2-z{x}^3$
(vi) $x^5{y}^7-8x^3{y}^8+10x^4{y}^4{z}^4$

Q.

Write the following polynomial in standard form:

$2x^3+5x-x^2-x^5$

Q.

In a polynomial, the exponents of the variables are always:

1. Integers

2. Non - negative integers

3. Rational numbers

4. Negative integers

Q. Find the degree of the polynomial $4a^4-2(3+a^4-ab+4b^3)-2a^4$.

1. 1
2. 2
3. 4
4. 3

Q. Find the degree of the polynomial expression $7x^5+2x^4+6x^8$.

1. $6$
2. $5$
3. $4$
4. $8$

Q. Find the degree of the polynomial $\frac{21x}{3x}+2$.

1. 1
2. 9
3. 0
4. Not a polynomial

Q.

In a polynomial, the exponents of the variables are always:

1. Non - negative integers

2. Positive integers

3. Non - positive integers

4. Integers

Q. For what value of $k$ the polynomial $4x^2-kx+9$ is a perfect square.

Q.

Write the following polynomial in standard form:

$2x^4-\frac{4}{3}x+3x^2+2$

Q. What is the degree of a quadratic polynomial?

1. $0$
2. $1$
3. $2$
4. $3$

Q. (6x³+3x)/ by 3x . Find the degree of the quotient .

Q. What is the degree of the given polynomial?

$2x^3+4x^2+5$

1. 2
2. 4
3. 3
4. 5

Q. The degree of the polynomial $30x^2+45x^3+2x^5+8x^6+x^7$ is 3.

1. True
2. False

Q.

Write the degree of each polynomial given below:

(i) $xy+7z$ (ii) $x^2-6x^3+8$

(iii) $y-6y^2+5y^8$ (iv) $xyz-3$

(v) $xy+y{z}^2-z{x}^3$ (vi) $x^5{y}^7-8x^3{y}^8+10x^4{y}^4{z}^4$

Q. Find the degree of the polynomial $4y+7+\frac{x^{\frac{5}{2}}y}{x^{\frac{1}{2}}}+2x^2$.

1. 1
2. 2
3. 3
4. Not a polynomial

Q. Write down the degree of the following polynomial:

1. 3
2. 4
3. 5
4. 1

Q. What is the degree of the polynomial $\frac{7x^2+2x^5+4x}{3x}?$

1. $2$
2. $3$
3. $4$
4. $5$

Q. Verify the polynomial geometrically: $(x+y+z{)}^2$

Q. Identify which of the following expressions are polynomials. If so, write their degrees.
$4a^3{b}^2-3a{b}^4+5ab+2/3$

Q.

Which of the following expressions are polynomials?
(i) $x^2+4$
(ii) $4-x^{-1}$
(iii) $2x^2-\frac{2}{x}$

1. i

2. i, ii, iii

3. iii

4. ii, iii