Question

Given an example of polynomial p(x),g(x),q(x) and r(x),which satisfy the division algorithm and degree q(x)=degree r(x)

Answer 1

☆☆ranshsangwan☆☆☆

deg q(x) = deg r(x)

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