Question

Question 5 (iii)
Give examples of polynomial p(x), g(x), q(x) and r(x), which satisfy the division algorithm and

deg r(x) = 0

Answer 1

Let p(x) = $x^3$ + 1 and g(x) = $x^2$

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

Clearly, the degree of r(x) is 0.

Checking for division algorithm,

p(x) = g(x) $\times$ q(x) + r(x)

$x^3+1=\left(x^2\right)\times x+1$ = $x^3+1=x^3+1$

Thus, the division algorithm is satisfied.