Degree of a polynomial is the highest power of the variable in the polynomial.

(i) Degree of quotient will be equal to degree of dividend when divisor is constant.

Let us assume the division of by 2.

Here, p(x) =

g(x) = 2

q(x) = and r(x) = 0

Degree of p(x) and q(x) is the same i.e., 2. Checking for division algorithm,

p(x) = g(x) × q(x) + r(x)

=

Thus, the division algorithm is satisfied.

(ii) Let us assume the division of x³+ x by x²,

Here,

p(x) = x³+ x

g(x) = x²

q(x) = x and r(x) = x

Clearly, the degree of q(x) and r(x) is the same i.e., 1. Checking for division algorithm,

p(x) = g(x) × q(x) + r(x) x³ + x

= (x² ) × x + x x³ + x = x³ + x

Thus, the division algorithm is satisfied.

(iii) Degree of remainder will be 0 when remainder comes to a constant.

Let us assume the division of x³+ 1by x².

Here,

p(x) = x³+ 1 g(x) = x²

q(x) = x and r(x) = 1

Clearly, the degree of r(x) is 0. Checking for division algorithm,

p(x) = g(x) × q(x) + r(x)x³ + 1

= (x² ) × x + 1 x³ + 1 = x³ +1

Thus, the division algorithm is satisfied.