Question

If p(x)=g(x)q(x)+r(x) then the degree of r(x) is


Choose the correct option


Less than q(x)


Greater than 0 and less than q(x)


Less than p(x)


None of these.​

Answer 1

Answer:

Answer

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

We know the formula,

Dividend = Divisor x quotient + Remainder

p(x)=g(x)×q(x)+r(x)

So here the degree of quotient will be equal to degree of dividend when the divisor is constant.

Let us assume the division of 4x2 by 2.

Here, p(x)=4x2

g(x)=2

q(x)= 2x2 and r(x)=0

Degree of p(x) and q(x) is the same i.e., 2.

Checking for division algorithm,

p(x)=g(x)×q(x)+r(x)

4x2=2(2x2)

Hence, the division algorithm is satisfied.

(ii) 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

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

Hence, the division algorithm is satisfied.

(iii) deg r(x) = 0

Degree of remainder will be 0 when remainder comes to a constant.

Let us assume the division of x4+1 by x3

Here, p(x) = x4+1

g(x) = x3

q(x)=x and r(x)=1

Degree of r(x) is 0.

Checking for division algorithm,

Step-by-step explanation:

hope it will be helpful