Question

can (x-1) be the remainder on division of a polynomial, p(x) by (2x+3)? justify your answer​

Answer 1

Answer:

(x-1) can not be the remainder

Step-by-step explanation:

Dividend = p(x) (Given)

Divisor = 2x + 3 (Given)

According to the division algorithm =

Dividend = divisor × quotient + remainder

Where,

Remainder = r(x) = 0 and the degree of r ( x ) < degree of divisor

Degree of the divisor = 1  --- eq (1)

Remainder = r(x) = x - 1

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

Thus equation, ( 1 ) = ( 2 ) it is possible

Thus, as per the remainder theorem  the degree of the remainder is less than the degree of divisor but here  reminder = x-1 , it's degree is 1,therefore , x - 1 is not the Remainder of p(x).