Question

Can x – 1 be the remainder on division of a polynomial p (x) by 2x + 3? Justify your answer

Answer 1

Hi

By division algorithm:

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Dividend = divisor × quotient +

remainder
Where,

Remainder = r ( x ) = 0 or


Degree of r ( x ) < degree of divisor

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According to the problem,

Dividend = p ( x )

Divisor = 2x + 3

Degree of the divisor = 1 ------(1)

Remainder = r ( x ) = x - 1

Degree of the remainder = 1-------(2)

( 1 ) = ( 2 ) it is possible

Therefore ,

x - 1 is not the Remainder of p ( x )

I hope this will useful to you.

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Answer 2

Answer:

By remainder theorem,

degree of the remainder is less than the degree of divisor

But here

remainder = x -1

its degree is 1

and

divisor2x +3

its degree is 1

it is wrong

Therefore........

n-1 is not remainder of p (x)