. Give examples of polynomials

Best Answer

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

(i) deg p(x) = deg q(x)

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

Let us assume the division of 6x²+2x+2 by 2.

Here, p(x) =  6x²+2x+2 by 2.

Thus, the division algorithm is satisfied.

(iii)deg r(x) = 0

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.