Question

if x3 + 1 is divided by x2 + 5, then the possible degree of quotient is
O (a) 0
O (b) 1
O (c) 2
O (d) 3​

Answer 1

Answer:

If x³+1 is divided by x²+5, then degree of the quotient is 1. because first term of quotient is x³/x²=x.

Hence, your answer is 1.

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

if x³ + 1 is divided by x² + 5 , then the possible degree of quotient is

(a) 0

(b) 1

(c) 2

(d) 3

CONCEPT TO BE IMPLEMENTED

Division Algorithm :

Let f(x) and g(x) be two polynomials of degree n and m respectively and n ≥ m . Then there exist two uniquely determined polynomials q(x) and r(x) satisfying

f(x) = g(x) q(x) + r(x)

Where the degree of q(x) is n - m and r(x) is either a zero polynomial or the degree of r(x) is less than m

EVALUATION

Let f(x) = x³ + 1

g(x) = x² + 5

Degree of f(x) = 3

Degree of g(x) = 2

So by the Division Algorithm ,

Degree of q(x)

= 3 - 2

= 1

Hence the possible degree of quotient is 1

FINAL ANSWER

Hence the correct option is (b) 1

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