Question

Can (x-7) be the reminder on division of a polynomial P(x)by(7x+2)? Justify your answer

Answer 1

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 = 7x + 2

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

Remainder = r ( x ) = x - 7

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

( 1 ) = ( 2 ) it is possible

Therefore ,

x - 7is not the Remainder of p ( x )