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If fourth degree polynomial is divided by a quadratic polynomial, write the degree of the remainder.

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1 or 0

1 or 2

answer is A.

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Detailed Solution

Given that a fourth degree polynomial is divided by a quadratic polynomial.
Division algorithm is given by

f (x) = g (x) q (x) − r (x),

where

f (x)

is the dividend,

g (x)

is the divisor,

q (x)

is the quotient and

r (x)

is the remainder.
Let the fourth degree polynomial be

f x = a x 4 + b x 3 + c x 2 + d x + e

and the quadratic polynomial be

g (x) = ∣ x 2 + m x + n

.
Therefore, degree of quotient

q (x)

4 − 2 = 2

Let the remainder be

r x

.
By remainder theorem,

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

Here, possible values of degree of

r x

are 1, when the remainder is a linear expression or 0, when the remainder is a constant or 0.
Therefore, degree of

r x

will be 1 or 0.
Hence the correct option is 1.

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