Question

What is the remainder on dividing the polynomial p(x) by ax + b? What is condition under which ax + b is a factor of the polynomial p(x)?

Answer 1

Remainder theorem states that when a polynomial p(x) is divided by (x − a), the remainder obtained is p(a).

Divisor = ax + b

ax + b =

=

The remainder obtained on dividing p(x) by is.

Thus, the remainder obtained on dividing p(x) by ax + b is.

Factor theorem says that for the polynomial p(x) and for the number a, if we have p(a) = 0, then (x − a) is a factor of p(x).

For (ax + b) to be a factor of the polynomial p(x), p should be equal to 0.