Question

Which of the following is not correct, when a polynomial is divided by another polynomial using: Dividend = Divisor × Quotient + Remainder

A) Remainder = 0
B) degree of remainder is less than the divisor
C) degree of remainder is more than the divisor
D) none of the above

Answer 1

The incorrect option is C) degree of remainder is more than the divisor, as it goes against the rules of polynomial division which state that the degree of the remainder must be less than the degree of the divisor.

Step-by-step explanation:

When a polynomial is divided by another polynomial, the relationship is given by: Dividend = Divisor × Quotient + Remainder. The incorrect statement among the options given is C) degree of remainder is more than the divisor. When dividing polynomials, the degree of the remainder must always be less than the degree of the divisor.

If it were greater, the division would not be complete, and there would be additional terms to divide by the divisor.

Option A) is correct because when a polynomial divides another polynomial evenly, with no leftover terms, the remainder is indeed zero. Option B) is also correct as it reflects the rule of polynomial division that the degree of the remainder is less than the degree of the divisor. Therefore, Option C) is the non-conforming statement.