Question

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

deg q(x) = deg r(x)

Answer 1

Let $p\left(x\right)$ = $x^3$ + $x$ and $g\left(x\right)$ = $x^2$

$q\left(x\right)=x$, and $r\left(x\right)=x$

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)

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

$x^3+x=x^3+x$

Thus, the division algorithm is satisfied.