Question

Write the degree of the given polynomials.

(i) $\sqrt{5}$ (ii)$x^{°}$ (iii) $x^2$ (iv) $\sqrt{2}{m}^{10}-7$ (v) $2p-\sqrt{7}$ (vi) $7y-y^3+y^5$ (vii) $xyz+xy-z$ (viii) $m^3{n}^7-3m^{5}n+mn$

Answer 1

The highest power of the variable in a polynomial of one variable is called the degreee of the polynomial. Also, the highest sum of the powers of the variables in each term of the polynomial in more than one variable is the degree of the polynomial.

(i)
$\sqrt{5}=\sqrt{5}\times 1=\sqrt{5}{x}^0$

The degree of the polynomial $\sqrt{5}$ is 0.

(ii)
The degree of the polynomial x⁰ is 0.

(iii)
The degree of the polynomial x² is 2.

(iv)
The degree of the polynomial $\sqrt{2}{m}^{10}-7$ is 10.

(v)
The degree of the polynomial $2p-\sqrt{7}$ is 1.

(vi)
The degree of the polynomial $7y-y^3+y^5$ is 5.

(vii)
The sum of the powers of the variables in the polynomial $xyz+xy-z$ are 1 + 1 + 1 = 3 and 1 + 1 = 2.

The degree of the polynomial $xyz+xy-z$ is 3.

(viii)
The sum of the powers of the variables in the polynomial $m^3{n}^7-3m^{5}n+mn$ are 3 + 7 = 10, 5 + 1 = 6 and 1 + 1 = 2.

The degree of the polynomial $m^3{n}^7-3m^{5}n+mn$ is 10.