Question

6)
Give examples of polynomials p(x), g(x), q(x) and r(x) which satisfy the division algorithm and
i) deg p(x) = deg q (x)
ii) deg g(x) = 2 and deg r(x)=0​

Answer 1

Answer:

pls note

Step-by-step explanation:

degree p(x) = deg q(x).

Then we have to find p(x), g(x), q(x) & r(x)

Let us consider g(x)=–1 and p(x)=–x +2=>–(x–2)

Then,

q(x)+ r(x) = p(x)/g(x) = –(x–2)/–1 = (x–2) + 0

So, q(x) = (x–2) and r(x)=0,

Hence, degree of p(x)=–(x–2) is 1 and degree of q(x)=(x–2) is 1

deg q(x) = deg r(x)

Let us consider g(x)=x–1 and p(x) = x²–2

Then,

q(x) + r(x) = p(x)/g(x) = (x²–2)/(x–1)

q(x) + r(x) =(x²–2.x.1+1+ 2x –3)/(x–1)

q(x) + r(x) = {(x–1)²+(2x–3)}/(x–1)

q(x) + r(x) = (x–1) + (2x–3)/(x–1)

So, q(x) = (x–1) and r(x) = 2x –3)

Hence,degree q(x) = degree r(x) = 1

deg r(x) = 0

Let us consider g(x)=1 and p(x) = x +1

Then,

q(x) + r(x) = p(x)/g(x) = (x+1)/1 = (x+1) + 0

So, q(x) = (x–1) and r(x) = 0

Hence, degree r(x) = 0.