Question

QUESTION 5
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Answer 1

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

Let us assume the division of

→ 6x2 + 2x + 2 by 2

→ p(x) = 6x2 + 2x + 2

→ g(x) = 2

→ q(x) = 3x2 + x + 1

→ r(x) = 0

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

Checking for division algorithm,

p(x) = g(x) × q(x) + r(x)

→ 6x2 + 2x + 2 = 2x (3x2 + x + 1)

division algorithm is satisfied.

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

Let us assume the division of

→ x3+ x by x2,

→ p(x) = x3 + x

→ g(x) = x2

→ q(x) = x and r(x) = x

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)

→ x3 + x = (x2 ) × x + x

→ x3 + x = x3 + x

the division algorithm is satisfied.

(iii) deg r(x) = 0

Let us assume the division of

→ x3+ 1 by x2.

→ p(x) = x3 + 1

→ g(x) = x2

→ q(x) = x and r(x) = 1

the degree of r(x) is 0.

Checking for division algorithm

→ p(x) = g(x) × q(x) + r(x)

→ x3 + 1 = (x2 ) × x + 1

→ x3 + 1 = x3 + 1

the division algorithm is satisfied......

                                                                                                                             

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Answer 2

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