# Polynomials

#### Question 5:

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

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

(ii) deg
*q*(*x*)
= deg *r*(*x*)

(iii) deg
*r(x*) = 0

#### Answer:

According
to the division algorithm, if *p*(*x*) and *g*(*x*)
are two polynomials with

*g*(*x*)
≠ 0, then we can find polynomials *q*(*x*) and *r*(*x*)
such that

*p*(*x*)
= *g*(*x*) × *q*(*x*) + *r*(*x*),

where
*r*(*x*) = 0 or degree of *r*(*x*) <
degree of *g*(*x*)

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 ( i.e., when any polynomial i...

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