Which of the following is a polynomial?

1. $x - \dfrac{1}{x}$

2. $x + \sqrt{x}$

3. $\dfrac{x}{\sqrt{2}} - \dfrac{1}{\sqrt[3]{2}}$

4. $x^{\dfrac{1}{2}} + x^{\dfrac{-1}{2}}$

Which of the following has the highest degree?

1. $x^5 + 2x^5$

2. $2^8$

3. $-\dfrac{3a^3b^2c}{4}$

4. $\dfrac{7a^6b^5}{-5a^3b^4}$

The sum of the polynomials bn - 8am - 8cp, 5cp - am + 2bn and 6am + 5bn - 3cp is equal to

1. -2am + 2bn - 4cp
2. -2am + 8bn - 2cp
3. -3am + 2bn - 4cp
4. -3am + 8bn - 6cp

Fill in the blanks :

(i) The highest power of the …………… in a polynomial is called its degree.

(ii) The degree of the polynomial 7⁵ is …………… .

(iii) Several parts of an algebraic expression separated by + or - signs are called the …………… of the expression.

(iv) Any number is a polynomial of degree …………… .

(v) Terms having the same …………… are called like terms.

(vi) The algebraic expression for the statement ‘the number of times b is contained in x' is …………… .

(vii) 1 + x + y + xy is a polynomial having …………… terms and degree ………….. .

(viii) The length of a side of a square having perimeter 8x² - 2y + 16xy is …………… .

(ix) In a polynomial, the exponents of the variables are always …………… .

(x) If the length of a rectangle having perimeter (6 m² - 2 mn + 2 m²n - 4n²) units, is (3m² + m²n - 2 mn) units, then its breadth is equal to …………… units.